<PAGE>
 
                                                                    EXHIBIT 99.4

                   AMENDMENT TO REGISTRATION RIGHTS AGREEMENT
                   ------------------------------------------


     This Amendment to Registration Rights Agreement (this "Agreement") is
entered into as of September 25, 1997 by and between Bradley Real Estate, Inc.,
a Maryland corporation (the "Company") and County Line 31 Company, L.P.
("Contributor").

     WHEREAS, pursuant to a Contribution Agreement dated June 20, 1997 by and
between Contributor and Bradley Operating Limited Partnership (the "Operating
Partnership"), Contributor received units of limited partnership interest
("Units") in the Operating Partnership, which may be redeemed for cash or, at
the option of the Company, for the number of shares of the Company's common
stock, $.01 par value ("Common Stock"), issuable pursuant to the Operating
Partnership's Second Restated Agreement of Limited Partnership (the "Partnership
Agreement").

     WHEREAS, Contributor is distributing Units to (i) the individual partners
of Contributor listed on Schedule A of the Registration Rights Agreement dated
                         ----------                                           
as of July 31, 1998 (the "Registration Rights Agreement") or (ii) the estates or
beneficiaries of the estates of deceased partners of Contributor (each such
holder of Units, including Contributor, is individually referred to herein as a
"Holder" and collectively as the "Holders").

     WHEREAS, in connection with the distribution of the Units the Company has
requested an amendment to the Registration Rights Agreement to conform that
agreement with several other similar agreements entered into by the Company.

     NOW, THEREFORE, in consideration of the mutual promises and agreements set
forth herein, and other valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, the parties hereto hereby agree as follows:

     The first sentence of Section 1 of the Registration Rights Agreement is
hereby deleted and the following is replaced therefor:

          The Company will use its reasonable efforts to (i) file a registration
          statement with the Securities and Exchange Commission (the "SEC")
          under Rule 415 under the Securities Act of 1933 (the "Securities Act")
          relating to the issuance to the Holders of all shares of Common Stock
          issuable upon the redemption or in exchange for their Units (a "Shelf
          Registration Statement") within fourteen (14) days after the first
          date upon which the Units may be redeemed, and (ii) cause such Shelf
          Registration Statement to be declared effective by the SEC as soon as
          practical thereafter.

     Except as specifically amended hereby, the Registration Rights Agreement
remains in full force and effect.

                                      (i)

<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of 
the date first written above.


                                    BRADLEY REAL ESTATE, INC.

                                    By: /s/ Thomas P. D'Arcy
                                        ---------------------------------
                                        Name:  Thomas P. D'Arcy
                                        Title: President

                                     (ii)
<PAGE>
 
                         Registration Rights Agreement
                             Holder Signature Page



                                    COUNTY LINE 31 COMPANY, L.P.


                                    By: /s/ John A. Wallace
                                        ------------------------------
                                        Name:  John A. Wallace
                                        Title: General Partner and
                                               Member of Executive Committee


                                    Address for Notice:
                                    c/o F.C. Tucker Company, Inc.
                                    9279 N. Meridian Street, Suite 100
                                    Indianapolis, Indiana 46260

                                     (iii)
<PAGE>
 
                         REGISTRATION RIGHTS AGREEMENT
                         -----------------------------


     This Registration Rights Agreement (this "Agreement") is entered into as of
July 31, 1997 by and between Bradley Real Estate, Inc., a Maryland corporation
(the "Company") and County Line 31 Company, L.P. ("Contributor").

     WHEREAS, pursuant to a Contribution Agreement dated June 20, 1997 by and
between Contributor and Bradley Operating Limited Partnership (the "Operating
Partnership"), Contributor will receive units of limited partnership interest
("Units") in the Operating Partnership, which may be redeemed for cash or, at
the option of the Company, for the number of shares of the Company's common
stock, $.01 par value ("Common Stock"), issuable pursuant to the Operating
Partnership's Amended and Restated Agreement of Limited Partnership (the
"Partnership Agreement").

     WHEREAS, Contributor may after the expiration of the Holding Period (as
defined in that certain Admission of Limited Partnership Agreement dated of even
date between Contributor, the Company and the Operating Partnership) distribute
such Units to (i) the individual partners of  Contributor listed on Schedule A
                                                                    ----------
attached hereto or (ii) the estates or beneficiaries of the estates of deceased
partners of Contributor (each such holder of Units, including Contributor, is
individually referred to herein as a "Holder" and collectively as the
"Holders").

     NOW, THEREFORE, in consideration of the mutual promises and agreements set
forth herein, and other valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, the parties hereto hereby agree as follows:

     1.   Registration.
          ------------ 

     (a) Registration Statement Covering Issuance of Common Stock.  The Company
         --------------------------------------------------------              
will use its efforts to (i) file a registration statement with the Securities
and Exchange Commission (the "SEC") under Rule 415 under the Securities Act of
1933 (the "Securities Act") relating to the issuance to the Holders of all
shares of Common Stock issuable upon the redemption or in exchange for their
Units (a "Shelf Registration Statement"), and (ii) cause such Shelf Registration
Statement to be declared effective by the SEC prior to the first date upon which
the Units may be redeemed.  The Company agrees to use its reasonable efforts to
keep such Shelf Registration Statement (or in the event such initial Shelf
Registration Statement is withdrawn or terminated for any reason, to keep a
successor Shelf Registration Statement) continuously effective until such time
as all of the Units have been redeemed for cash or, at the option of the
Company, for the number of shares of Common Stock issuable pursuant to the
Partnership Agreement.  In the event that the Company is unable to cause such
Shelf Registration Statement to be declared effective by the SEC or is unable to
keep such Shelf Registration Statement effective until such time as all of the
Units have been redeemed for cash 

                                      (i)
<PAGE>
 
or, at the option of the Company, for the number of shares issuable pursuant to
the Partnership Agreement, then each Holder shall have the rights set forth in
Section 1(b) and 1(c) below.
 
     (b)  Demand Registration.
          ------------------- 

          (i) After the first date upon which Units held by the Holders may be
redeemed until the date on which there are no Registrable Shares (as hereinafter
defined) remaining, subject to the conditions set forth in this Agreement,
including without limitation the conditions set forth in Section 1(b)(ii) below,
any Holder or Holders may request that the Company cause to be filed a
registration statement (a "Demand  Registration Statement") under Rule 415 under
the Securities Act relating to the sale by such Holders of their previously or
concurrently issued Registrable Shares in accordance with the terms hereof.  As
used in this Agreement, the term "Registrable Shares" means shares of Common
Stock issued or to be issued to the Holders upon redemption or in exchange for
their Units, excluding (A) Common Stock for which a Registration Statement
relating to the issuance or sale thereof shall have become effective under the
Securities Act and which have been issued or sold, as applicable, under such
Registration Statement, (B) Common Stock sold pursuant to Rule 144 under the
Securities Act or (C) Common Stock which, together with all other Registrable
Shares held by such Holder and any other Holder whose sales of Registrable
Shares must be aggregated with sales of such Holder pursuant to Rule 144(e), is
eligible for sale pursuant to Rule 144(e) under the Securities Act.  Upon
receipt of any such request, the Company shall give written notice of such
proposed registration to all Holders of Units and Registrable Shares.  Such
Holders shall have the right, by giving written notice to the Company within
fifteen (15) business days after such notice referred to in the preceding
sentence has been given by the Company to elect to have included in the Demand
Registration Statement such of their Registrable Shares as each Holder may
request in such notice of election.  Thereupon, the Company shall use reasonable
efforts to cause such Demand Registration Statement to be filed and declared
effective by the SEC for all Registrable Shares which the Company has been
requested to register as soon as practicable thereafter.  The Company agrees to
use reasonable efforts to keep the Demand Registration Statement continuously
effective until the earliest of (a) the date on which the Holders no longer hold
any Registrable Shares registered under the Demand Registration Statement, (b)
the date on which the Registrable Shares registered under the Demand
Registration Statement held by each Holder may, together with all other
Registrable Shares held by such Holder and any other Holder whose sales of
Registrable Shares must be aggregated with sales of such Holder pursuant to Rule
144(e), be sold by such Holder pursuant to Rule 144(e) under the Securities Act
or (c) the date which is twelve (12) months from the effective date of such
Demand Registration Statement.  The Company shall not be required to file and
effect a new Demand Registration Statement pursuant to this Section 1(b) until a
period of twelve (12) months has elapsed from the termination of the
registration statement with respect to Registrable Shares covered by a prior
registration request.

          (ii) The Company shall have no obligation under Section 1(b)(i) unless
the following conditions are satisfied:

                                     (ii)
<PAGE>
 
     Any Holder who requests that the Company cause to be filed a Demand
Registration Statement pursuant to Section 1(b)(i) must provide to the Company a
certificate (the "Authorizing Certificate") that sets forth (i) the name and
address of the Holder, (ii) the number of Registrable Shares owned by such
Holder, and, if different, the number of Registrable Shares such Holder has
elected to have registered, (iii) the number of all shares of Common Stock of
the Company (including the Registrable Shares) owned by such Holder, (iv) the
number of shares of Common Stock if any of such Holder that are not being
registered and that will be owned by such Holder after the sale of all shares to
be registered, (v) a certification from each such Holder that it is requesting
the registration of only those shares of Common Stock received by such Holder
upon the redemption of its Units pursuant to the Partnership Agreement, and (vi)
such further information as the Company may reasonably request in connection
with such Registration Statement. If the Company determines that a Holder's
shares of Common Stock have become eligible for sale pursuant to Rule 144(e),
the Company shall, at the request of such Holder, deliver to such Holder an
opinion of counsel to such effect.

     (c) Piggyback Registration.  If at any time after the first date upon which
         ----------------------                                                 
Units held by the Holders may be redeemed and until the date on which there are
no Registrable Shares remaining the Company proposes to file a registration
statement under the Securities Act with respect to an offering of Common Stock
solely for cash (other than a registration statement (i) on Form S-8 or any
successor form or in connection with any employee or director welfare, benefit
or compensation plan, (ii) on Form S-4 or any successor form or in connection
with an exchange offer, (iii) in connection with a rights offering or a dividend
reinvestment and share purchase plan offered exclusively to existing holders of
Common Stock, (iv) in connection with an offering solely to employees of the
Company or its affiliates, (v) relating to a transaction pursuant to Rule 145 of
the Securities Act, or (vi) a shelf registration on Form S-3 or any successor
form), whether or not for its own account (a "Piggyback Registration
Statement"), the Company shall give to the Holders of Units and Registrable
Shares written notice of such proposed filing at least ten (10) business days
before filing.  The notice referred to in the preceding sentence shall offer
Holders the opportunity to register such amount of Registrable Shares as each
Holder may request (a "Piggyback Registration").  Subject to the provisions of
Section 2 below, the Company shall include in such Piggyback Registration all
Registrable Shares requested to be included in the registration for which the
Company has received an Authorizing Certificate within five (5) business days
after the notice referred to above has been given by the Company to the Holders.
Holders of Registrable Shares shall be permitted to withdraw all or part of the
Registrable Shares from a Piggyback Registration at any time prior to the
effective date of such Piggyback Registration.  If a Piggyback Registration is
an underwritten registration on behalf of the Company and the managing
underwriter advises the Company that the total number of shares of Common Stock
requested to be included in such registration exceeds the number of shares of
Common Stock which can be sold in such offering, the Company will include in
such registration in the following priority:  (i) first, all shares of Common
Stock the Company proposes to sell and (ii) second, up to the full number of
applicable Registrable Shares requested to be included in such registration
which, in the opinion of such managing underwriter, can be sold without
adversely affecting the price range 

                                      (iii)
<PAGE>
 
or probability of success of such offering, which shall be allocated among the
Holders requesting registration and all other stockholders requesting
registration on a pro rata basis. No Registrable Securities or other shares of
Common Stock requested to be included in a registration pursuant to demand
registration rights shall be excluded from the underwriting unless all
securities other than such securities are first excluded. Any Demand
Registration Statement, Piggyback Registration Statement or Shelf Registration
Statement is sometimes referred to as a "Registration Statement."

     2.   Registration Procedures.
          ----------------------- 

     (a) The Company shall notify each Holder of the effectiveness of any
applicable Registration Statement and shall furnish to each Holder with respect
to a Shelf Registration Statement, a copy of the prospectus included therein or,
with respect to a Demand Registration Statement or a Piggyback Registration
Statement, such number of copies of the Registration Statement (including any
amendments, supplements and exhibits), the prospectus contained therein
(including each preliminary prospectus), any documents incorporated by reference
in the Registration Statement and such other documents as such Holder may
reasonably request in order to facilitate its sale of the Registrable Shares in
the manner described in the Registration Statement.

     (b) The Company shall prepare and file with the SEC from time to time such
amendments and supplements to the Registration Statement and prospectus used in
connection therewith as may be necessary to keep the Registration Statement
effective and to comply with the provisions of the Securities Act with respect
to the issuance or disposition of all the Registrable Shares until the earlier
of (i) such time as all of the Registrable Shares have been issued or disposed
of in accordance with the intended methods of issuance by the Company, or
disposition by the Holders, as set forth in the Registration Statement or (ii)
the date on which the Registration Statement ceases to be effective in
accordance with the terms of Section 1. Upon ten (10) business days' notice, the
Company shall file any supplement or post-effective amendment to the
Registration Statement with respect to such Holder's interests in or plan of
distribution of Registrable Shares that is reasonably necessary to permit the
sale of the Holder's Registrable Shares pursuant to the Registration Statement
and the Company shall file any necessary listing applications or amendments to
the existing applications to cause the shares to be then listed or quoted on the
primary exchange or quotation system on which the Common Stock is then listed or
quoted.  The Company agrees to deliver copies of the prospectus as contained in
such Registration Statement promptly following effectiveness thereof to the New
York Stock Exchange (or any other applicable national securities exchange) as
contemplated by SEC Rule 157.

     (c) The Company shall promptly notify each Holder of, and confirm in
writing, any request by the SEC for amendments or supplements to the
Registration Statement or the prospectus related thereto or for additional
information.  In addition, the Company shall promptly respond to such SEC
requests and shall promptly notify each Holder of, and confirm in writing, the
filing of the Registration Statement, any prospectus supplement related thereto

                                      (iv)
<PAGE>
 
or any post-effective amendment to the Registration Statement and the
effectiveness of any post-effective amendment.

     (d) The Company shall promptly notify each Holder, at any time when a
prospectus relating to the Registration Statement is required to be delivered
under the Securities Act, of the happening of any event as a result of which the
prospectus included in the Registration Statement, as then in effect, includes
an untrue statement of a material fact or omits to state any material fact
required to be stated therein or necessary to make the statements therein, in
light of the circumstances under which they were made, not misleading. In such
event and subject to paragraph 7 of this Agreement, the Company shall promptly
prepare and furnish to each Holder a reasonable number of copies of a supplement
to or an amendment of such prospectus as may be necessary so that, as thereafter
delivered to the purchasers of Registrable Shares, such prospectus shall not
include an untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary to make the statements therein, in
light of the circumstances under which they are made, not misleading.

     3.   State Securities Laws.  Subject to the conditions set forth in this
          ---------------------                                              
Agreement, the Company shall, promptly upon the filing of a Registration
Statement including Registrable Shares, file such documents as may be necessary
to register or qualify the Registrable Shares under the securities or "Blue Sky"
laws of such states as any Holder may reasonably request to the extent that
registration or qualification under such laws is necessary in order that the
Registrable Shares may be legally sold in such states, and the Company shall use
reasonable efforts, in the case of a Demand Registration Statement or a
Piggyback Registration Statement, and best efforts, in the case of a Shelf
Registration Statement, to cause such filings to become effective; provided,
                                                                   -------- 
however, that with respect to a Demand Registration Statement or a Piggyback
-------                                                                     
Registration Statement, the Company shall not be obligated to qualify as a
foreign corporation to do business under the laws of any such state in which it
is not then qualified or to file any general consent to service of process in
any such state.  Once effective, the Company shall use reasonable efforts, in
the case of a Demand Registration Statement or a Piggyback Registration
Statement, and best efforts, in the case of a Shelf Registration Statement, to
keep such filings effective until the earlier of (a) such time as all of the
Registrable Shares have been issued by the Company, or disposed of in accordance
with the intended methods of disposition by the Holder, as set forth in the
Registration Statement, (b) in the case of a particular state, a Holder has
notified the Company that it no longer requires effective filing in such state
in accordance with its original request for filing or (c) the date on which the
Registration Statement ceases to be effective with the SEC.  The Company shall
promptly notify each Holder of, and confirm in writing, the receipt by the
Company of any notification with respect to the suspension of the qualification
of the Registrable Shares for sale under the securities or "Blue Sky" laws of
any jurisdiction or the initiation or threat of any proceeding for such purpose.

     4.   Expenses.  The Company shall bear all expenses incurred in connection
          --------                                                             
with the registration of the Registrable Shares pursuant to Section 1(a) and
Section 1(c) of this Agreement.  In addition, the Company will pay all expenses
in connection with the registration 

                                      (v)
<PAGE>
 
of Registrable Shares pursuant to Section 1(b) of this Agreement provided that
the registration is for One Million Dollars or more of Registerable Shares. The
Holders shall bear their ratable share of all expenses incurred by the Company
in connection with a registration in which the Holders are included pursuant to
Section 1(b) of this Agreement based on the number of Registrable Shares
included to the total number of shares of Common Stock so registered for each
Registration Statement registering less than the applicable amount specified in
the previous sentence for such Holder. Such expenses shall include, without
limitation, all printing, legal and accounting expenses incurred by the Company
and all registration and filing fees imposed by the SEC, any state securities
commission or the New York Stock Exchange or, if the Common Stock is not then
listed on the New York Stock Exchange, the principal national securities
exchange or national market system on which the Common Stock is then traded or
quoted. Holders shall be responsible for any brokerage or underwriting
commissions and taxes of any kind (including, without limitation, transfer
taxes) with respect to any disposition, sale or transfer of Registrable Shares
and for any legal, accounting and other expenses incurred by them in connection
with any Registration Statement.

     5.   Indemnification by the Company.  In connection with any Demand
          ------------------------------                                
Registration Statement or any Piggyback Registration Statement, the Company
agrees to indemnify each of the Holders and their respective officers,
directors, employees, agents, representatives and affiliates, and each person or
entity, if any, that controls a Holder within the meaning of the Securities Act,
and each other person or entity, if any, subject to liability because of his,
her or its connection with a Holder, and any underwriter and any person who
controls the underwriter within the meaning of the Securities Act (an
"Indemnitee") against any and all losses, claims, damages, actions, liabilities,
costs and expenses (including without limitation reasonable attorneys' fees,
expenses and disbursements documented in writing), joint or several, arising out
of or based upon any untrue or alleged untrue statement of material fact
contained in the Registration Statement or any prospectus contained therein, or
any omission or alleged omission to state therein a material fact required to be
stated therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading, except insofar as and
to the extent that such statement or omission arose out of or was based upon
information regarding the Indemnitee or its plan of distribution which was
furnished in writing by such Indemnitee to the Company expressly for use
therein, provided, further that the Company shall not be liable to any person
who participates as an underwriter in the offering or sale of Registrable Shares
or any other person, if any, who controls such underwriter within the meaning of
the Securities Act, in any such case to the extent that any such loss, claim,
damage, liability (or action or proceeding in respect thereof) or expense arises
out of or is based upon (i) an untrue statement or alleged untrue statement or
omission or alleged omission made in such Registration Statement, any such
preliminary prospectus, final prospectus, summary prospectus, amendment or
supplement in reliance upon and in conformity with information furnished in
writing by such Indemnitee to the Company expressly for use in connection with
the Registration Statement or the prospectus contained therein by such
Indemnitee or (ii) such Indemnitee's failure to send or give a copy of the final
prospectus furnished to it by the Company at or prior to the time such action is
required by the Securities Act to the person claiming an untrue statement or
alleged untrue statement or omission or 

                                     (vi)
<PAGE>
 
alleged omission if such statement or omission was corrected in such final
prospectus. The obligations of the Company under this Section 5 shall survive
the completion of any offering of Registrable Shares pursuant to a Registration
Statement under this Agreement or otherwise and shall survive the termination of
this Agreement.

     6.   Covenants of Holders.  Each of the Holders hereby agrees to cooperate
          --------------------                                                 
with the Company and to furnish to the Company all such information in
connection with the preparation of the Registration Statement and any filings
with any state securities commissions as the Company may reasonably request. In
connection with any Demand Registration Statement or any Piggyback Registration
Statement, each Holder hereby agrees, (a) to the extent required by the
Securities Act, to deliver or cause delivery of the prospectus contained in the
Registration Statement to any purchaser of the shares covered by the
Registration Statement from the Holder, (b) to notify the Company of any sale of
Registrable Shares by such Holder and (c) to indemnify the Company, its
officers, directors, employees, agents, representatives and affiliates, and each
person, if any, who controls the Company within the meaning of the Securities
Act, and each other person, if any, subject to liability because of his
connection with the Company, against any and all losses, claims, damages,
actions, liabilities, costs and expenses arising out of or based upon (i) any
untrue statement or alleged untrue statement of material fact contained in
either the Registration Statement or the prospectus contained therein, or any
omission or alleged omission to state therein a material fact required to be
stated therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading, if and to the extent
that such statement or omission arose out of or was based upon information
regarding the Holder or its plan of distribution which was furnished in writing
by such Indemnitee to the Company expressly for use therein, or (ii) the failure
by the Holder to deliver or cause to be delivered the prospectus contained in
the Registration Statement (as amended or supplemented, if applicable)
previously furnished by the Company to the Holder to any purchaser of the shares
covered by the Registration Statement from the Holder. Notwithstanding the
foregoing, (i) in no event will a Holder have any obligation under this Section
6 for amounts the Company pays in settlement of any such loss, claim, damage,
liability or action if such settlement is effected without the consent of the
Holder (which consent shall not be unreasonably withheld) and (ii) the total
amount for which a Holder shall be liable under this Section 6 shall not in any
event exceed the aggregate proceeds received by him or it from the sale of the
Holder's Registrable Shares in such registration. The obligations of the Holders
under this Section 6 shall survive the completion of any offering of Registrable
Shares pursuant to a Registration Statement under this Agreement or otherwise
and shall survive the termination of this Agreement.

     7.   Suspension of Registration Requirement.
          -------------------------------------- 

     (a) The Company shall promptly notify each Holder of, and confirm in
writing, the issuance by the SEC of any stop order suspending the effectiveness
of any applicable Registration Statement or the initiation of any proceedings
for that purpose.  The Company shall use reasonable efforts to obtain the
withdrawal of any order suspending the effectiveness of the Registration
Statement as soon as practicable.

                                     (vii)
<PAGE>
 
     (b) Notwithstanding anything to the contrary set forth in this Agreement,
the Company's obligation under this Agreement to use reasonable efforts to cause
the Registration Statement and any filings with any state securities commission
to be made or to become effective or to amend or supplement the Registration
Statement shall be suspended in the event and during such period as the Chief
Executive Officer of the Company or its Board of Directors determines in good
faith that pending negotiations relating to, or consummation of, a transaction
or the occurrence of an event that would require additional disclosure of
material information by the Company in the Registration Statement or such filing
(such circumstances being hereinafter referred to as a "Suspension Event") that
would make it impractical or unadvisable to cause the Registration Statement or
such filings to be made or to become effective or to amend or supplement the
Registration Statement; provided, however, that such suspension shall continue
only as long as such event or its effect is continuing and has not otherwise
been publicly disclosed and in no event will that suspension exceed sixty (60)
days. The Company agrees not to exercise the rights set forth in this Section
7(b) more than twice in any twelve month period. The Company shall notify the
Holder of the existence of any Suspension Event.

     (c) Each holder of Registrable Shares whose Registrable Shares are covered
by a Demand Registration Statement or a Piggyback Registration Statement filed
pursuant to Section 1 hereof agrees, if requested by the managing underwriter or
underwriters in an underwritten offering (an "Underwritten Offering"), not to
effect any public sale or distribution of any of the securities of the Company
of any class included in such Underwritten Offering, including a sale pursuant
to Rule 144 or Rule 144A under the Securities Act (except as part of such
Underwritten Offering), during the 15-day period prior to, and during the 90-day
period (or such longer period as may be required by the managing underwriter or
underwriters) beginning on, the date of pricing of each Underwritten Offering
(the "Underwritten Offering Period"), to the extent timely notified in writing
by the managing underwriters.  The Company agrees that the rights set forth in
this Section 7(c) may not be exercised more than once in any six month period or
within six months of the Company exercising its rights under Section (7)(b)
above. Furthermore, notwithstanding anything to the contrary set forth in this
Agreement, the Company's obligation under this Agreement to use reasonable
efforts to cause a Demand Registration Statement or a Piggyback Registration
Statement and any filings with any state securities commission in connection
therewith to be made or to become effective or to amend or supplement such
Registration Statement shall be suspended in the event and during such period as
the Company is proceeding with an Underwritten Offering if the Company is
advised by the underwriters that the sale of Registrable Shares under such
Registration Statement would have a material adverse effect on the Underwritten
Offering.

     8.   Black-Out Period.  Following the effectiveness of any Registration
          ----------------                                                  
Statement and the filings with any state securities commissions in connection
therewith, the Holders agree that they will not effect any sales of the
Registrable Shares pursuant to such Registration Statement or any such filings
at any time after they have received notice from the Company to suspend sales
(i) as a result of the occurrence or existence of any Suspension Event, (ii)
during the Underwritten Offering Period of any Underwritten Offering, or (iii)
so that the Company 
                    
                                    (viii)
<PAGE>
 
may promptly correct or update the Registration Statement or such filing
pursuant to Section 2(c) or 2(d). The Holder may recommence effecting sales of
the Registrable Shares pursuant to the Registration Statement or such filings
following further notice to such effect from the Company, which notice shall be
given by the Company not later than five (5) business days after the conclusion
of any such Suspension Event or Underwritten Offering Period or the correction
of the Registration Statement, as applicable.

     9.   Additional Shares.  The Company, at its option, may register, under
          -----------------                                                  
any Registration Statement and any filings with any state securities commissions
filed pursuant to this Agreement, any number of unissued shares of Common Stock
(including, without limitation, shares of Common Stock which may be issued to
any of the Holders of Units in the Operating Partnership) or any shares of
Common Stock owned by any other shareholder or shareholders of the Company.

     10.  Contribution.  If the indemnification provided for in Sections 5 and 6
          ------------                                                          
is unavailable to an indemnified party with respect to any losses, claims,
damages, actions, liabilities, costs or expenses referred to therein or is
insufficient to hold the indemnified party harmless as contemplated therein,
then the indemnifying party, in lieu of indemnifying such indemnified party,
shall contribute to the amount paid or payable by such indemnified party as a
result of such losses, claims, damages, actions, liabilities, costs or expenses
in such proportion as is appropriate to reflect the relative fault of the
Company, on the one hand, and the Holder, on the other hand, in connection with
the statements or omissions which resulted in such losses, claims, damages,
actions, liabilities, costs or expenses as well as any other relevant equitable
considerations.  The relative fault of the Company, on the one hand, and of the
Holder, on the other hand, shall be determined by reference to, among other
factors, whether the untrue or alleged untrue statement of a material fact or
omission to state a material fact relates to information supplied by the Company
or by the Holder and the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent such statement or omission;
provided, however, that in no event shall the obligation of any indemnifying
--------  -------                                                           
party to contribute under this Section 10 exceed the amount that such
indemnifying party would have been obligated to pay by way of indemnification if
the indemnification provided for under Sections 5 or 6 hereof had been available
under the circumstances.

     The Company and the Holders agree that it would not be just and equitable
if contribution pursuant to this Section 10 were determined by pro rata
allocation or by any other method of allocation that does not take account of
the equitable considerations referred to in the immediately preceding paragraph.
Notwithstanding the provision of this Section 10, no Holder shall be required to
contribute any amount in excess of the amount by which the gross proceeds from
the sale of the shares of Common Stock of such Holder exceeds the amount of any
damages that such Holder otherwise has been required to pay by reason of such
untrue or alleged untrue statement or omissions.

                                      (ix)
<PAGE>
 
     No indemnified party guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any indemnifying party who was not guilty of such fraudulent
misrepresentation.

     11.  No Other Obligation to Register.  Except as otherwise expressly
          -------------------------------                                
provided in this Agreement, the Company shall have no obligation to the Holders
to register the Registrable Shares under the Securities Act.

     12.  Amendments and Waivers.  The provisions of this Agreement may not be
          ----------------------                                              
amended, modified or supplemented without the prior written consent of the
Company and Holders holding in excess of 75% of the Registrable Shares (or
Partnership Units redeemable or exchangeable for Registrable Shares); and any
amendment, modification or supplement consented to by the Company and the
Holders of a majority of such registrable Shares (or of such Partnership Units)
shall bind all such Holders.

     13.  Notices.  Except as set forth below, all notices and other
          -------                                                   
communications provided for or permitted hereunder shall be in writing and shall
be deemed to have been duly given if delivered personally or sent by telex or
telecopier, registered or certified mail (return receipt requested), postage
prepaid or courier or overnight delivery service to the Company at the following
address and to the Holder at the address set forth on his or her signature page
to this Agreement (or at such other address for any party as shall be specified
by like notice, provided that notices of a change of address shall be effective
only upon receipt thereof), and further provided that in case of directions to
amend the Registration Statement pursuant to Section 2(b) or Section 6(b), a
Holder must confirm such notice in writing by overnight express delivery with
confirmation of receipt:

     If to the Company:  Bradley Real Estate, Inc.
                         40 Skokie Boulevard
                         Northbrook, IL  60062
                         Attn: Thomas P. D'Arcy
                               President
 
                         Telephone:  (847) 272-9800
                         Telecopy:   (847) 480-1893
 
                         With a copy to:
 
                         Goodwin, Procter & Hoar LLP
                         Exchange Place
                         Boston, MA 02109
                         Attn:  William B. King, P.C.
 
                         Telephone:  (617) 570-1000
                         Telecopy:   (617) 523-1231

                                      (x)
<PAGE>
 
In addition to the manner of notice permitted above, notices given pursuant to
Sections 1, 7 and 8 hereof may be effected telephonically and confirmed in
writing thereafter in the manner described above.

     14.  Successors and Assigns.  This Agreement shall be binding upon and
          ----------------------                                           
inure to the benefit of the successors and assigns of the Company. This
Agreement may only be assigned to a transferee of all or a portion of the
Holder's Units in compliance with the Partnership Agreement or a transferee of
all or a portion of the Holder's Registrable Securities which constitute
"restricted securities" in the hands of such transferee, as defined in Rule 144
under the Securities Act. Any attempted assignment other than to a transferee of
all or a portion of a Holder's Units in compliance with the Partnership
Agreement or a transferee of all or a portion of the Holder's Registrable
Securities which constitute "restricted securities" in the hands of such
transferee, as defined in Rule 144 under the Securities Act, will be void and of
no effect and shall terminate all obligations of the Company hereunder with
respect to such Holder.

     15.  Counterparts.  This Agreement may be executed in any number of
          ------------                                                  
counterparts and by the parties hereto in separate counterparts, each of which
when so executed shall be deemed to be an original and all of which taken
together shall constitute one and the same agreement.

     16.  Governing Law.  This Agreement shall be governed by and construed in
          -------------                                                       
accordance with the laws of the State of Maryland applicable to contracts made
and to be performed wholly within said State.

     17.  Severability.  In the event that any one or more of the provisions
          ------------                                                      
contained herein, or the application thereof in any circumstances, is held
invalid, illegal or unenforceable in any respect for any reason, the validity,
legality and enforceability of any such provision in every other respect and of
the remaining provisions contained herein shall not be in any way impaired
thereby, it being intended that all of the rights and privileges of the parties
hereto shall be enforceable to the fullest extent permitted by law.

     18.  Entire Agreement.  This Agreement is intended by the parties as a
          ----------------                                                 
final expression of their agreement and intended to be the complete and
exclusive statement of the agreement and understanding of the parties hereto in
respect of the subject matter contained herein.  There are no restrictions,
promises, warranties or undertakings, other than those set forth or referred to
herein, with respect to such subject matter.  This Agreement supersedes all
prior agreements and understandings between the parties with respect to such
subject matter.

                  [Remainder of Page Intentionally Left Blank]

                                     (xi)
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date first written above.


                                    BRADLEY REAL ESTATE, INC.


                                    By: /s/ Thomas P. D'Arcy
                                        ----------------------------------
                                            Name: Thomas P. D'Arcy
                                            Title:   President



                                     (xii)
<PAGE>
 
                         REGISTRATION RIGHTS AGREEMENT
                             HOLDER SIGNATURE PAGE


                                    COUNTY LINE 31 COMPANY, L.P.


                                    By: /s/ John A. Wallace
                                        ------------------------------------
                                        Name:  John A. Wallace
                                        Title: General Partner and Member
                                               of Executive Committee
 
                                          Address for Notice:

                                          c/o F.C. Tucker Company
                                          2500 One American Square
                                          Indianapolis, Indiana 46282

                                    (xiii)
<PAGE>
 
                                   SCHEDULE A
                                   ----------


                  CONSTITUENT PARTNERS AND PERMITTED ASSIGNEES
                  --------------------------------------------
                        OF COUNTY LINE 31 COMPANY, L.P.
                        -------------------------------


                                                      Percentage of
                Name and Address                   Interest and Units
 
----------------------------------------------------------------------
Robert W. Wilds (or Charitable Remainder Trust)           50.0%
8250 Woodfield Crossing Blvd.
Suite 100
Indianapolis, IN 46240-4348
----------------------------------------------------------------------
Robert E. Houk, Trustee of Revocable Grantor               5.5%
Trust
6111 Spring Mill Road
Indianapolis, IN 46228
----------------------------------------------------------------------
John A. Wallace                                            5.5%
125 Prestwick Circle
Vero Beach, FL 32967
----------------------------------------------------------------------
J. Kurt Mahrdt, Jr.                                        3.0%
714 North Capitol
Indianapolis, IN 46204
----------------------------------------------------------------------
George C. Charbonneau                                      3.0%
(or Linda A. Charbonneau, his wife)
2500 One American Square
Box 82055
Indianapolis, IN 46282-0002
----------------------------------------------------------------------
James T. Schrage                                           3.0%
1299 West 86th Street
Indianapolis, IN 46260
----------------------------------------------------------------------
Gary B. Warstler                                           3.0%
9279 N. Meridian Street
Indianapolis, IN 46260
----------------------------------------------------------------------
John R. Jewett                                             3.0%
2500 One American Square
Box 82055
Indianapolis, IN 46282-0002
----------------------------------------------------------------------

                                      (xv)
<PAGE>
 
----------------------------------------------------------------------
Maurice C. Martindale                                      3.0%
1243 Windswept Avenue
Naples, FL 33942
----------------------------------------------------------------------
Hans T. French                                             3.0%
6279 Tri-Ridge Blvd.
Loveland, OH 45140
----------------------------------------------------------------------
Roy G. Altman                                              2.5%
9279 N. Meridian St
Suite 100
Indianapolis, IN 46260
----------------------------------------------------------------------
Don E. Ellis                                               2.0%
2406 Anthony Avenue
Clearwater, FL 34619
----------------------------------------------------------------------
Fred C. Tucker III, Trustee                                5.5%
U/W of Fred C. Tucker, Jr.
2500 One American Square
Box 82055
Indianapolis, IN 46282-0002
----------------------------------------------------------------------
Polly Boleman Jameson, Co-Trustee                          5.5%
of Trust U/W of Edward J. Boleman
1608 Northwood Drive
Indianapolis, IN 46240
----------------------------------------------------------------------
David J. Backer, Trustee                                   2.5%
Herbert J. Backer Trust                                    ----
8710 N. Meridian Street
Indianapolis, IN 46260
 
----------------------------------------------------------------------
TOTAL                                                      100%
----------------------------------------------------------------------

                                     (xvi)