Exhibit 24.2 POWER OF ATTORNEY I, Mark Byrne, being a director of White Mountains Insurance Group, Ltd. hereby appoint and constitute K. Thomas Kemp and Gordon S. Macklin, and each of them singly, my true and lawful attorneys with full power to them, and each of them singly, to sign for me and in my name any and all amendments (including post-effective amendments) to this registration statement (or to any other registration statement for the same offering that is to be effective upon filing pursuant to Rule 462(b) under the Securities Act), and generally to do all such things in my name and in my capacity as a director to enable White Mountains Insurance Group, Ltd. to comply with the provisions of the Securities Act of 1933 and all requirements of the Securities and Exchange Commission, hereby ratifying and confirming my signature as it may be signed by my said attorneys, or any of them, to said registration statement and any and all amendments thereto. Pursuant to the requirements of the Securities Act of 1933, this registration statement has been signed by me as a director of White Mountains Insurance Group, Ltd. on the date indicated: Dated this 7th Day of December, 2001. SIGNED /s/ Mark Byrne ---------------------------- Name: Mark Byrne