Exhibit 10.1

SHARE PURCHASE AGREEMENT

THIS SHARE PURCHASE AGREEMENT (this ‘‘Agreement’’) is made as of May 13, 2008,
between Candover Investments plc (‘‘Candover Investments’’), Candover (Trustees)
Limited (‘‘Candover Trustees’’), Candover 2001 GmbH & Co. KG (‘‘Candover
GmbH’’), Halifax EES Trustees International Limited as trustee of the Candover
2001 Employee Benefit Trust (‘‘Halifax’’), Candover Partners Limited (‘‘Candover
Partners’’) in its capacity as general partner of the Candover 2001 Fund US No.
1 Limited Partnership (‘‘Candover Fund US 1’’), Candover 2001 Fund US No. 2
Limited Partnership (‘‘Candover Fund US 2’’), Candover 2001 Fund US No. 3
Limited Partnership (‘‘Candover Fund US 3’’), Candover 2001 Fund US No. 4
Limited Partnership (‘‘Candover Fund US 4’’), Candover 2001 Fund US No. 5
Limited Partnership (‘‘Candover Fund US 5’’), Candover 2001 Fund UK No. 3
Limited Partnership (‘‘Candover Fund UK 3’’), Candover 2001 Fund UK No. 4
Limited Partnership (‘‘Candover Fund UK 4’’), Candover 2001 Fund UK No. 5
Limited Partnership (‘‘Candover Fund UK 5’’), and Candover 2001 Fund UK No. 6
Limited Partnership (‘‘Candover Fund UK 6,’’ and collectively with Candover
Investments, Candover Trustees, Candover GmbH, Halifax, Candover Partners,
Candover Fund US 1, Candover Fund US 2, Candover Fund US 3, Candover Fund US 4,
Candover Fund US 5, Candover Fund UK 3, Candover Fund UK 4, and Candover Fund UK
5 ‘‘Sellers,’’ and each individually a ‘‘Seller’’), and Aspen Insurance Holdings
Limited (the ‘‘Company’’).

WHEREAS, (i) Candover Investments is the beneficial owner of 681,398 ordinary
shares, par value 0.15144558 cents per share, of the Company (the ‘‘Shares’’),
(ii) Candover Trustees is the beneficial owner of 30,996 Shares, (iii) Candover
GmbH is the beneficial owner of 133,826 Shares, (iv) Halifax is the beneficial
owner of 16,794 Shares (v) Candover Partners as a general partner of Candover
Fund US 1 is the beneficial owner of 965,390 Shares, (vi) Candover Partners as a
general partner of Candover Fund US 2 is the beneficial owner of 608,511 Shares,
(vii) Candover Partners as a general partner of Candover Fund US 3 is the
beneficial owner of 343,070 Shares, (viii) Candover Partners as a general
partner of Candover Fund US 4 is the beneficial owner of 97,182 Shares, (ix)
Candover Partners as a general partner of Candover Fund US 5 is the beneficial
owner of 406,054 Shares, (x) Candover Partners as a general partner of Candover
Fund UK No.1 Limited Partnership is the beneficial owner of 747,593 Shares, (xi)
Candover Partners as a general partner of Candover Fund UK No. 2 Limited
Partnership is the beneficial owner of 317,982 Shares, (xii) Candover Partners
as a general partner of Candover Fund UK 3 is the beneficial owner of 1,018,463
Shares, (xiii) Candover Partners as a general partner of Candover Fund UK 4 is
the beneficial owner of 100,654 Shares, (xiv) Candover Partners as a general
partner of Candover Fund UK 5 is the beneficial owner of 70,911 Shares and (xv)
Candover Partners as a general partner of Candover Fund UK 6 is the beneficial
owner of 552,463 Shares; and

WHEREAS, in a privately negotiated transaction, the Company desires to
repurchase (i) 681,398 Shares from Candover Investments, (ii) 30,996 Shares from
Candover Trustees, (iii) 133,826 Shares from Candover GmbH, (iv) 16,794 Shares
from Halifax, (v) 965,390 Shares from Candover Partners as a general partner of
Candover Fund US 1, (vi) 608,511 Shares from Candover Partners as a general
partner of Candover Fund US 2, (vii) 343,070 Shares from Candover Partners as a
general partner of Candover Fund US 3, (viii) 97,182 Shares from Candover
Partners as a general partner of Candover Fund US 4, (ix) 406,054 Shares from
Candover Partners as a general partner of Candover Fund US 5, (x) 73,551 Shares
from Candover Partners as a general partner of Candover Fund UK 3, (xi) 100,654
Shares from Candover Partners as a general partner of Candover Fund UK 4, (xii)
70,911 Shares from Candover Partners as a general partner of Candover Fund UK 5
and (xiii) 552,463 Shares from Candover Partners as a general partner of
Candover Fund UK 6, for a total of 4,080,800 Shares, and the Sellers have agreed
to such Share repurchase by the Company on the terms and conditions hereinafter
set forth.

--------------------------------------------------------------------------------

NOW, THEREFORE, THE PARTIES HEREBY AGREE AS FOLLOWS:

[spacer.gif] [spacer.gif] [spacer.gif] 1.  Repurchase of Shares.

1.1.    Repurchase. Subject to the terms and conditions of this Agreement, the
Company agrees to purchase from each Seller at the Closing (as defined below),
and each Seller hereby consents and agrees to the Company’s respective purchase
at the Closing of (i) 681,398 Shares from Candover Investments, (ii) 30,996
Shares from Candover Trustees, (iii) 133,826 Shares from Candover GmbH. (iv)
16,794 from Halifax and (v) 3,217,786 Shares from Candover Partners as a general
partner of Candover US Fund 1, Candover US Fund 2, Candover US Fund 3, Candover
US Fund 4, Candover US Fund 5, Candover UK Fund 3, Candover UK Fund 4, Candover
UK Fund 5, and Candover UK Fund 6, each for a purchase price in cash of $24.505
per share, for an aggregate purchase price of (i) $16,697,658 for the Candover
Investments Shares, (ii) $759,557 for the Candover Trustees Shares, (iii)
$3,279,406 for the Candover GmbH Shares, (iv) $411,537 for the Halifax Shares
and (v) $78,851,845 for the Shares from Candover Partners as a general partner
of Candover US Fund 1, Candover US Fund 2, Candover US Fund 3, Candover US Fund
4, Candover US Fund 5, Candover UK Fund 3, Candover UK Fund 4, Candover UK Fund
5, and Candover UK Fund 6, respectively, for a total purchase price of
$100,000,004 (the ‘‘Purchase Price’’).

1.2.    Closing. The purchase and sale of the Shares shall take place at the
offices of Dewey & LeBoeuf New York, New York at 10 AM on May 19, 2008 or at
such other date, time and place as agreed between the Sellers and the Company
(the ‘‘Closing’’).

1.3.    Closing Deliveries by Seller. At the Closing, Sellers shall deliver, or
cause to be delivered, to the Company any share certificates representing the
Shares, for cancellation by the Company.

1.4.    Closing Deliveries by the Company. At the Closing, the Company shall
deliver, or cause to be delivered, to each Seller their respective portion of
the Purchase Price for their Shares. Each portion of the Purchase Price shall be
paid by wire transfer of immediately available funds in U.S dollars to the
account designated by the relevant Seller to the Company in writing on the date
of this Agreement. Upon such delivery of the Purchase Price, the Company shall
amend its register of members to reflect its purchase of the Shares.

2.    Representations and Warranties of Seller. Each Seller hereby represents
and warrants to the Company that:

2.1.    Authorization. All acts and conditions required by law or otherwise on
the part of Seller to authorize the execution and delivery of this Agreement by
Seller and the transactions contemplated herein and the performance of all
obligations of Seller hereunder have been duly performed and obtained, and this
Agreement constitutes a valid and legally binding obligation of Seller,
enforceable in accordance with its terms, subject, as to the enforcement of
remedies, to applicable bankruptcy, insolvency, moratorium, reorganization or
similar laws affecting creditors’ rights generally and to general equitable
principles.

2.2.    Title to Stock. Seller has good and marketable title to the Shares, free
and clear of all liens, pledges, encumbrances, equities, security interests and
claims whatsoever, and assuming the Company purchases the Shares for value in
good faith and without notice of any such lien, pledges, encumbrance, equity,
security interest or other adverse claim within the meaning of the New York
Uniform Commercial Code, the Shares will be free and clear of all liens,
pledges, encumbrances, equities, security interests and claims whatsoever.

2.3.    Broker’s or Finder’s Fees. Seller has not authorized any person to act
as a broker, finder or in any other similar capacity in connection with the
transactions contemplated by this Agreement.

2.4.    Non-Contravention. The transactions contemplated by this Agreement do
not violate any blue sky law of a state of the United States or securities law
of any jurisdiction.

3.    Representations and Warranties of the Company. The Company hereby
represents and warrants to each Seller that:

2

--------------------------------------------------------------------------------

3.1.    Authorization. All acts and conditions required by law or otherwise on
the part of the Company to authorize the execution and delivery of this
Agreement by Company and the transactions contemplated herein and the
performance of all obligations of the Company hereunder have been duly performed
and obtained, and this Agreement constitutes a valid and legally binding
obligation of the Company, enforceable in accordance with its terms, subject, as
to the enforcement of remedies, to applicable bankruptcy, insolvency,
moratorium, reorganization or similar laws affecting creditors’ rights generally
and to general equitable principles.

3.2.    Broker’s or Finder’s Fees. The Company has not authorized any person to
act as a broker, finder or in any other similar capacity in connection with the
transactions contemplated by this Agreement.

3.3.    Non-Contravention. The transactions contemplated by this Agreement do
not violate any blue sky law of any state of the United States or securities law
of any jurisdiction.

4.    Covenants.

4.1.    Further Assurances. Sellers and the Company hereby agree to execute and
deliver such certificates, instruments and other documents, and to take other
actions, as may be reasonably requested by any other party hereto in order to
carry out, evidence or give effect to the transactions contemplated by this
Agreement.

4.2.    Tax. Each Seller agrees to pay their respective portion of any tax
imposed in connection with the repurchase of the Shares as contemplated under
this Agreement.

4.3.    Expenses. Except as otherwise agreed by Sellers and the Company, Sellers
and the Company shall each pay their own expenses incurred in connection with
the transactions contemplated by this Agreement.

5.    Conditions of the Company’s Obligations at Closing. The obligations of the
Company to purchase the Shares are subject to the fulfillment on or before the
Closing of each of the following conditions:

5.1.    Representations and Warranties. The representations and warranties of
each Seller contained in Section 2 shall be true on and as of the Closing with
the same effect as though such representations and warranties had been made on
and as of the date of such Closing.

5.2.    Performance. Each Seller shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing.

6.    Conditions of Sellers’ Obligations at Closing. The consent of Sellers to
the Company’s repurchase of the Shares under this Agreement are subject to the
fulfillment on or before the Closing of each of the following conditions by the
Company:

6.1.    Representations and Warranties. The representations and warranties of
the Company contained in Section 3 shall be true on and as of the Closing with
the same effect as though such representations and warranties had been made on
and as of the Closing.

6.2.    Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing.

7.    Miscellaneous.

7.1.    Survival. The representations and warranties of Sellers or the Company
contained in or made pursuant to this Agreement shall survive the Closing.

7.2.    Successors and Assigns. Except as otherwise provided herein, the terms
and conditions of this Agreement shall inure to the benefit of and be binding
upon the respective successors of the parties. Nothing in this Agreement,
express or implied, is intended to confer upon any party other than the parties
hereto or their respective successors any rights, remedies, obligations, or
liabilities

3

--------------------------------------------------------------------------------

under or by reason of this Agreement, except as expressly provided in this
Agreement. No party may assign its rights under this Agreement without the prior
written consent of the other parties.

7.3.    Governing Law. This Agreement shall be governed by and construed under
the laws of the State of New York without regard to conflicts of law principles.

7.4.    Counterparts. This Agreement may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument. This Agreement may be
executed and delivered by facsimile or e-mail transmission.

7.5.    Amendments and Waivers. Any term of this Agreement may be amended and
the observance of any term of this Agreement may be waived (either generally or
in a particular instance and either retroactively or prospectively), only with
the written consent of Seller and the Company.

7.6.    Severability. If one or more provisions of this Agreement are held to be
unenforceable under applicable law, such provision shall be excluded from this
Agreement and the balance of the Agreement shall be interpreted as if such
provision were so excluded and shall be enforceable in accordance with its
terms. This Agreement comprises the entire agreement beween the parties on the
subject matter hereof.

[REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

4

--------------------------------------------------------------------------------

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

[spacer.gif]

[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif]
[spacer.gif]   [spacer.gif] [spacer.gif] CANDOVER INVESTMENTS PLC   [spacer.gif]
[spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew Moberly                  
[spacer.gif] [spacer.gif] Name:   Andrew Moberly   [spacer.gif] [spacer.gif]
Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif] CANDOVER (TRUSTEES)
LIMITED   [spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew
Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew Moberly  
[spacer.gif] [spacer.gif] Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif]
CANDOVER 2001 GMBH & CO. KG represented by DEUTSCHE CANDOVER (MANAGING LIMITED
PARTNER) GMBH   [spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/
Andrew Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew
Moberly   [spacer.gif] [spacer.gif] Title:   Attorney-in-Fact   [spacer.gif]
[spacer.gif] CANDOVER PARTNERS LIMITED as general partner for and on behalf of
CANDOVER 2001 FUND US No. 1 LIMITED PARTNERSHIP   [spacer.gif] [spacer.gif] By:
[spacer.gif] [spacer.gif] /s/ Andrew Moberly                   [spacer.gif]
[spacer.gif] Name:   Andrew Moberly   [spacer.gif] [spacer.gif]
Title:   Attorney-in-Fact

5

--------------------------------------------------------------------------------

[spacer.gif]

[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif]
[spacer.gif]   [spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED as general
partner for and on behalf of CANDOVER 2001 FUND US No. 2 LIMITED PARTNERSHIP  
[spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew
Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew Moberly  
[spacer.gif] [spacer.gif] Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif]
CANDOVER PARTNERS LIMITED as general partner for and on behalf of CANDOVER 2001
FUND US No. 3 LIMITED PARTNERSHIP   [spacer.gif] [spacer.gif] By: [spacer.gif]
[spacer.gif] /s/ Andrew Moberly                   [spacer.gif] [spacer.gif]
Name:   Andrew Moberly   [spacer.gif] [spacer.gif] Title:   Attorney-in-Fact  
[spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED as general partner for and
on behalf of CANDOVER 2001 FUND US No. 4 LIMITED PARTNERSHIP   [spacer.gif]
[spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew Moberly                  
[spacer.gif] [spacer.gif] Name:   Andrew Moberly   [spacer.gif] [spacer.gif]
Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED
as general partner for and on behalf of CANDOVER 2001 FUND US No. 5 LIMITED
PARTNERSHIP   [spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew
Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew Moberly  
[spacer.gif] [spacer.gif] Title:   Attorney-in-Fact

6

--------------------------------------------------------------------------------

[spacer.gif]

[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif]
[spacer.gif]   [spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED as general
partner for and on behalf of CANDOVER 2001 FUND UK No. 3 LIMITED PARTNERSHIP  
[spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew
Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew Moberly  
[spacer.gif] [spacer.gif] Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif]
CANDOVER PARTNERS LIMITED as general partner for and on behalf of CANDOVER 2001
FUND UK No. 4 LIMITED PARTNERSHIP   [spacer.gif] [spacer.gif] By: [spacer.gif]
[spacer.gif] /s/ Andrew Moberly                   [spacer.gif] [spacer.gif]
Name:   Andrew Moberly   [spacer.gif] [spacer.gif] Title:   Attorney-in-Fact  
[spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED as general partner for and
on behalf of CANDOVER 2001 FUND UK No. 5 LIMITED PARTNERSHIP   [spacer.gif]
[spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew Moberly                  
[spacer.gif] [spacer.gif] Name:   Andrew Moberly   [spacer.gif] [spacer.gif]
Title:   Attorney-in-Fact   [spacer.gif] [spacer.gif] CANDOVER PARTNERS LIMITED
as general partner for and on behalf of CANDOVER 2001 FUND UK No. 6 LIMITED
PARTNERSHIP   [spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew
Moberly                   [spacer.gif] [spacer.gif] Name:   Andrew Moberly  
[spacer.gif] [spacer.gif] Title:   Attorney-in-Fact

7

--------------------------------------------------------------------------------

[spacer.gif]

[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif]
[spacer.gif]   [spacer.gif] [spacer.gif] HALIFAX EES TRUSTEES INTERNATIONAL
LIMITED as trustee of the CANDOVER 2001 EMPLOYEE BENEFIT TRUST   [spacer.gif]
[spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Andrew Moberly                  
[spacer.gif] [spacer.gif] Name:   Andrew Moberly   [spacer.gif] [spacer.gif]
Title:   Attorney-in-Fact

8

--------------------------------------------------------------------------------

[spacer.gif]

[spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif] [spacer.gif]
[spacer.gif]   [spacer.gif] [spacer.gif] ASPEN INSURANCE HOLDINGS LIMITED  
[spacer.gif] [spacer.gif] By: [spacer.gif] [spacer.gif] /s/ Richard
Houghton                   [spacer.gif] [spacer.gif] Name:   Richard Houghton  
[spacer.gif] [spacer.gif] Title:   Chief Financial Officer

9

--------------------------------------------------------------------------------