<PAGE>   1
                                                                 Exhibit 4.35(d)

                      AMENDMENT NO. 4 TO THE RIGHTS AGREEMENT

              AMENDMENT NO. 4 TO THE RIGHTS AGREEMENT (this "Amendment"), dated
as of May 17, 2000, by and among NTL INCORPORATED, a Delaware corporation (the
"Company"), NTL HOLDINGS INCORPORATED, a Delaware corporation ("Second Holdco"),
which is a direct wholly owned subsidiary of the Company, and CONTINENTAL STOCK
TRANSFER & TRUST COM PANY, a New York corporation (the "Rights Agent") amends
the Rights Agreement (the "Rights Agreement"), dated October 13, 1993, as
amended pursuant to Amendment No. 1 to the Rights Agreement ("Amendment No.
1"), dated as of March 31, 1999, Amendment No. 2 to the Rights Agreement
("Amendment No. 2"), dated as of October 23, 1999, and Amendment No. 3 to the
Rights Agreement ("Amendment No. 3"), dated as of March 28, 2000, in each case
by and among the Company, the Rights Agent and the other party signatory
thereto, if any (collectively, the "Amended Rights Agreement"). Capitalized
terms used in this Amendment without definition shall have the meanings given to
them in the Amended Rights Agreement.

              WHEREAS, the Company and the Rights Agent entered into the Rights
Agreement specifying the terms of the Rights;

              WHEREAS, the Distribution Date has not occurred, and that
accordingly, the Company and the Rights Agent hereby amend the Amended Rights
Agreement in accordance with Section 27 thereof;

              WHEREAS, in accordance with Section 27 of the Amended Rights
Agreement, an authorized officer of the Company has delivered to the Rights
Agent an officer's certificate as to the compliance of this Amendment with the
terms and conditions contained in Section 27 of the Amended Rights Agreement;
and

              WHEREAS, on February 9, 2000, the Company, Second Holdco and
Holdings Merger Sub Inc., a Delaware corporation ("Second Merger Sub"), which is
a direct wholly owned subsidiary of Second Holdco and an indirect wholly owned
subsidiary of the Company, entered into an Agreement and Plan of Merger (the
"Second Merger Agreement"), pursuant to which, among other things, Second Merger
Sub shall be merged with and into the Company in accordance with Section 251(g)
of the General Corporation Law of the State of Delaware (the "Second Merger"),
with the Company continuing as the surviving corporation (the "Second Surviving
Corporation") and as a wholly owned subsidiary of Holdco.

              NOW, THEREFORE, in consideration of the premises and the mutual
agreements set forth in the Amended Rights Agreement and this Amendment, the
parties hereto intending to be legally bound hereby agree as follows:



<PAGE>   2



              Section 1. Incorporation of "Second Merger", "Second Merger
Agreement", "Second Merger Sub" and "Second Surviving Corporation" as Defined
Terms of the Amended Rights Agreement. The terms "Second Merger", "Second Merger
Agreement", "Second Merger Sub" and "Second Surviving Corporation" and the
respective definitions of such terms as set forth in the preamble of this
Amendment are hereby incorporated in the Amended Rights Agreement under the
heading "Certain Definitions" in Section 1 thereof.

              Section 2. Amendment to Definition of "Acquiring Person." Section
1(a) of the Amended Rights Agreement is hereby amended to add the following
sentence after the last sentence thereof which sentence was added pursuant to
Amendment No. 3: Notwithstanding the foregoing, neither Second Holdco nor any of
its Affiliates shall become an Acquiring Person as a result of the execution of
the Second Merger Agreement or the consummation of the Second Merger by filing
the Second Merger Agreement with the Secretary of State of the State of
Delaware.

              Section 3. Second Holdco as Successor to the Company. Pursuant to
Section 28 of the Amended Rights Agreement, upon consummation of the Second
Merger, all the covenants and provisions of the Amended Rights Agreement by or
for the benefit of the Company shall bind and inure to the benefit of Second
Holdco.

              Section 4. Rights Agreement as Amended. The term "Agreement" as
used in the Rights Agreement shall be deemed to refer to the Rights Agreement as
amended hereby and as previously amended by Amendment No. 1, Amendment No. 2 and
Amendment No. 3. Each of the foregoing amendments shall be effective as of their
respective dates and, except as set forth herein, the Rights Agreement shall
remain in full force and effect and shall be otherwise unaffected hereby. In the
event of any conflict or inconsistency between the provisions of this Amendment
on the one hand and the Rights Agreement or Amendment No. 1, Amendment No. 2 or
Amendment No. 3 on the other hand, with respect to the matters set forth herein
or contemplated hereby, the provisions of this Amendment shall govern such
conflict or inconsistency.

              Section 5. Counterparts. This Amendment may be executed in any
number of counterparts, and each of such counterparts shall for all purposes be
deemed an original, but all such counterparts shall together constitute but one
and the same agreement.

              Section 6. Governing Law. This Amendment shall be deemed to be a
contract made under the laws of the State of Delaware and for all purposes shall
be


                                        2

<PAGE>   3


governed by and construed in accordance with the laws of such State applicable
to contracts made and to be performed entirely within such State.

              Section 7. Descriptive Headings. Descriptive headings of the
several Sections of this Agreement are inserted for convenience only and shall
not control or affect the meaning or construction of any of the provisions
hereof.

              IN WITNESS WHEREOF, the parties hereto have caused this Amendment
to be duly executed by their authorized representative as of the date first
above written.


Attest:                                NTL INCORPORATED


By: /s/ LAUREN HOCHMAN BLAIR           By: /s/ RICHARD J. LUBASCH
   ---------------------------------     ---------------------------------------
   Name: Lauren Hochman Blair            Name:  Richard J. Lubasch
   Title: Assistant General Counsel      Title: Executive Vice President,
                                                  General Counsel and Secretary


Attest:                                NTL HOLDINGS INCORPORATED


By: /s/ LAUREN HOCHMAN BLAIR           By: /s/ RICHARD J. LUBASCH
   ---------------------------------     ---------------------------------------
   Name: Lauren Hochman Blair            Name:  Richard J. Lubasch
   Title: Assistant General Counsel      Title: Executive Vice President-
                                                  General Counsel and Secretary



Attest:                                CONTINENTAL STOCK TRANSFER & TRUST
                                       COMPANY, as Rights Agent


By: /s/ DONALD F. GROSS                By: /s/ MICHAEL J. NELSON
   ---------------------------------     ---------------------------------------
   Name: Donald F. Gross                 Name: Michael J. Nelson
   Title: Vice President                 Title: President


                                        3