<PAGE>
                                                                 Exhibit 3.1(k)


                            CERTIFICATE OF CORRECTION
                    TO THE CERTIFICATE OF DESIGNATION OF THE
                     VOTING POWERS, DESIGNATION, PREFERENCES
                    AND RELATIVE, PARTICIPATING, OPTIONAL OR
                    OTHER SPECIAL RIGHTS AND QUALIFICATIONS,
                       LIMITATIONS OR RESTRICTIONS OF THE
                           VARIABLE COUPON REDEEMABLE
                            PREFERRED STOCK, SERIES A
                               OF NTL INCORPORATED

                                   -----------

                        Pursuant to Section 103(f) of the
                        Delaware General Corporation Law
                                   -----------


                  NIL Incorporated (the "Corporation"), a corporation organized
and existing under and by virtue of the Delaware General Corporation Law (the
"DGCL"), does hereby certify as follows:

                  FIRST: On May 17, 2001, the Corporation filed a Certificate of
Designation for the Variable Coupon Redeemable Preferred Stock, Series A of the
Corporation (the "Certificate") in which the number of shares designated as
"Variable Coupon Redeemable Preferred Stock, Series A of NTL Incorporated" was
incorrectly set forth as 47,218 in paragraph (1) of the Certificate, which
created an inaccurate record of the corporate action.

                  SECOND: Specifically, the number of shares designated as
"Variable Coupon Redeemable Preferred Stock, Series A of NTL Incorporated"
should read, as corrected, 55,000. Accordingly, the text of paragraph (1) of the
Certificate shall be corrected to read in its entirety as follows:

                  "(1) Number and Designation. 55,000 shares of the Preferred
Stock shall be designated as "Variable Coupon Redeemable Preferred Stock, Series
A of NTL Incorporated", including, in the case of any reclassification,
recapitalization, or other change to such Preferred Stock or, in the case of a
consolidation or merger of the Corporation with or into another Person affecting
such Preferred Stock, such capital stock to which a Holder shall be entitled
upon the occurrence of such event (the "Variable-Coupon Redeemable Preferred
Stock, Series A"), and no other shares of Preferred Stock shall be designated as
"Variable Coupon Redeemable Preferred Stock, Series A". Any shares of Variable
Coupon Redeemable Preferred Stock; Series A redeemed or otherwise acquired by
the Corporation shall be retired and shall resume the status of authorized and
unissued shares of Preferred Stock, without designation as to series, until such
shares are once more designated as part of a particular series of Preferred
Stock by the Board of Directors."
<PAGE>
                  THIRD: This Certificate of Correction was prepared and
executed in accordance with Section 103(f) of the DGCL.

                  IN WITNESS WHEREOF, NTL Incorporated has caused this
Certificate of Correction to be duly executed in its corporate name this 18th
day of June 2001.

                                        NTL INCORPORATED


                                        By: /s/ Richard J. Lubasch
                                            -----------------------
                                        Name: Richard J. Lubasch
                                        Title: Executive Vice President,
                                        General Counsel and Secretary

                                       2