Exhibit (a)(1)(D)​

OFFER TO PURCHASE FOR CASH
by
WHITE MOUNTAINS INSURANCE GROUP, LTD.
of
UP TO $500 MILLION IN VALUE OF ITS COMMON SHARES
at a Purchase Price not greater than $1,400
nor less than $1,250 per Share

THE OFFER, PRORATION PERIOD AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF THE DAY ON SEPTEMBER 20, 2022, UNLESS THE OFFER IS EXTENDED (SUCH TIME, AS IT MAY BE EXTENDED, THE “EXPIRATION TIME”).

August 22, 2022​

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

We have been appointed by White Mountains Insurance Group, Ltd., a company organized under the laws of Bermuda (the “Company”), to act as Dealer Managers in connection with its offer to purchase up to $500 million in value of its outstanding common shares, par value $1.00 per share (the “Shares”), at a purchase price not greater than $1,400 nor less than $1,250 per Share, in cash, less any applicable withholding taxes and without interest, upon the terms and subject to the conditions set forth in the Offer to Purchase dated August 22, 2022 (the “Offer to Purchase”), and in the related Letter of Transmittal (the “Letter of Transmittal” and, together with the Offer to Purchase, as they may be amended or supplemented from time to time, the “Offer”). The Company may elect, but is not obligated, to purchase additional Shares pursuant to the Offer. The Offer is not conditioned upon the receipt of financing or any minimum number of Shares being properly tendered but is subject to certain other conditions.

The Company will determine a single per Share price, not greater than $1,400 nor less than $1,250 per Share, that it will pay for the Shares properly tendered and not properly withdrawn pursuant to the Offer, taking into account the number of Shares so tendered and the prices specified by tendering shareholders. The Company will select the lowest purchase price (in increments of $1.00) that will allow it to purchase up to $500 million in value of Shares at such price (or such lesser value depending on the number of Shares that are properly tendered and not properly withdrawn) pursuant to the Offer (subject to the Company’s right to purchase additional Shares as described in the Offer to Purchase). The Company will purchase all Shares properly tendered at prices at or below the purchase price and not properly withdrawn upon the terms and subject to the conditions set forth in the Offer to Purchase and the related Letter of Transmittal, including the provisions relating to “odd lot” tenders and proration described in the Offer to Purchase. All Shares so purchased by the Company will be purchased at the same price regardless of whether the shareholder tendered at a lower price. In the event that Shares representing more than $500 million in value are properly tendered in the Offer, the Company reserves the right to increase the number of Shares sought in the Offer by an amount not exceeding 2% of its outstanding Shares without extending the Expiration Time. In exercising this right, the Company may increase the Purchase Price to allow it to purchase all such additional shares. The Company also expressly reserves the right, in its sole discretion, to amend the Offer to purchase additional Shares, subject to applicable law. See Sections 1 and 14 of the Offer to Purchase. Shares tendered at prices in excess of the Purchase Price and Shares not purchased because of proration will be returned at the Company’s expense to the shareholders who tendered such Shares promptly following the Expiration Time.

Please 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 paid by the Company to the Information Agent, the Depositary and the Dealer Managers as described in the Offer to Purchase) 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;

(2)

Letter of Transmittal to be used by holders of Shares to tender Shares and for the information of your clients;

(3)

Letter from the Chief Executive Officer of the Company, G. Manning Rountree, to shareholders;

(4)

Form of Notice of Guaranteed Delivery to be used to accept the Offer and tender Shares pursuant to the Offer if the procedure for book-entry transfer cannot be completed by the Expiration Time or if all other required documents cannot be delivered to the Depositary by the Expiration Time;

(5)

Guidelines for Certification of Taxpayer Identification Number on Substitute Form W-9;

(6)

Letter that 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 Computershare Trust Company, N.A., the Depositary.

Shareholders must make their own decision as to whether to tender their Shares and, if so, how many Shares to tender and at what price or prices. Your clients should read carefully the information set forth or incorporated by reference in the Offer to Purchase and in the related Letter of Transmittal, including the Company’s purpose for making the Offer.

Certain conditions to the Offer are described in Section 8 of the Offer to Purchase. To be valid, all tenders must be in proper form as described in Section 2 of the Offer to Purchase.

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, at the end of the day on September 20, 2022, unless extended.

Under no circumstances will interest be paid on the purchase price of the Shares regardless of any extension of, or amendment to, the Offer or any delay in paying for such Shares.

None of the Company, our Board of Directors, the Dealer Managers, the Depositary or the Information Agent makes any recommendation as to whether any shareholder should tender Shares pursuant to the Offer or as to the purchase price or prices at which a shareholder may choose to tender them. Each of your clients must make their own decision after consulting with his or her own advisors whether to tender their Shares and, if so, how many Shares to tender and the price or prices at which they will tender them. In doing so, your clients should read carefully the information in the Offer, including the purposes and effects of the Offer.

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 D.F. King & Co., Inc. at (212) 269-5550 or by email at wtm@dfking.com.

Very truly yours,

J.P. Morgan Securities LLC

Barclays Capital Inc.

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU OR ANY OTHER PERSON THE AGENT OF THE COMPANY, THE DEPOSITARY, THE DEALER MANAGERS, THE INFORMATION AGENT OR ANY AFFILIATE OF THEM 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.