Exhibit 99.(a)(1)(D) WHITE MOUNTAINS INSURANCE GROUP, LTD. OFFER TO PURCHASE FOR CASH UP TO 1,500,000 OF ITS COMMON SHARES AT $165.00 NET PER SHARE THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON MONDAY, SEPTEMBER 18, 2000, UNLESS THE OFFER IS EXTENDED. August 21, 2000 To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees: We are enclosing herewith the material listed below relating to the offer by White Mountains Insurance Group, Ltd., a company organized under the laws of Bermuda (the "Company"), to purchase up to 1,500,000 of its outstanding Common Shares, par value $1.00 per share (the "Shares"), for cash at $165.00 per Share net to the seller, upon the terms and subject to the conditions set forth in the Offer to Purchase dated August 21, 2000, and in the related Letter of Transmittal (which together constitute the "Offer"). The Company may elect, but is not obligated, to purchase additional Shares pursuant to the Offer. THE OFFER IS NOT CONDITIONED UPON ANY MINIMUM NUMBER OF SHARES BEING VALIDLY TENDERED. We have been engaged by the Company as Information Agent with respect to the Offer. We are asking you to contact your clients for whom you hold Shares registered in your name (or in the name of your nominee) or who hold Shares registered in their own names. Please bring the Offer to their attention as promptly as possible. No fees or commissions (other than fees to the Information Agent and the Depositary as described in the Offer) will be payable to brokers, dealers or other persons for soliciting tenders of Shares pursuant to the Offer. The Company will, however, upon request, reimburse you for customary mailing and handling expenses incurred by you in forwarding any of the enclosed materials to your clients. No shareholders will be required to pay transfer taxes on the transfer to the Company of Shares purchased pursuant to the Offer, subject to Instruction 6 of the Letter of Transmittal. For your information and for forwarding to your clients, we are enclosing the following documents: (1) Offer to Purchase dated August 21, 2000; (2) Specimen Letter of Transmittal to be used by holders of Shares to tender Shares and for the information of your clients; (3) Letter from the Chairman of the Company, John J. Byrne, to shareholders. (4) Form of Notice of Guaranteed Delivery; (5) Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9; (6) Letter which may be sent to your clients for whose accounts you hold Shares registered in your name (or in the name of your nominee), with space provided for obtaining such clients' instructions with regard to the Offer; and (7) Return envelope addressed to Equiserve Trust Company, the Depositary. WE URGE YOU TO CONTACT YOUR CLIENTS PROMPTLY. PLEASE NOTE THAT THE OFFER, THE PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, ON MONDAY, SEPTEMBER 18, 2000, UNLESS EXTENDED. Your communications to shareholders with respect to the Offer will constitute your representation to the Company that (i) in connection with such communications you have complied with the applicable requirements of the Securities Exchange Act of 1934, as amended, and the applicable rules and regulations thereunder; (ii) if a foreign broker or dealer, you have conformed to the Rules of Fair Practice of the National Association of Securities Dealers, Inc. in making such communications; and (iii) in connection with such communications you have not used any offering materials other than those furnished by the Company. The Offer is not being made to (nor will tenders be accepted from or on behalf of) holders of Shares residing in any jurisdiction in which the making of the Offer or the acceptance thereof would not be in compliance with securities or Blue Sky laws of such jurisdiction. Additional copies of the enclosed material may be obtained from the undersigned. Any questions you may have with respect to the Offer should be directed to the undersigned at 1-888-756-1854. Very truly yours, Equiserve Trust Company NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY OTHER PERSON THE AGENT OF THE COMPANY, THE DEPOSITARY OR THE INFORMATION AGENT OR AUTHORIZE YOU OR ANY OTHER PERSON TO MAKE ANY STATEMENTS OR USE ANY MATERIAL ON BEHALF OF ANY OF THEM WITH RESPECT TO THE OFFER, OTHER THAN THE MATERIAL ENCLOSED HEREWITH AND THE STATEMENTS SPECIFICALLY CONTAINED IN SUCH MATERIAL.