A U.S. subsidiary of a British industrial holding company has offered to pay $15.3 million for a 24 percent stake in Washington Homes Inc. of Waldorf, Md.

Scottish Heritable Trust PLC has purchased an option to acquire 900,000 shares of Washington Homes common stock owned by Chairman William J. Harnett and President Lawrence M. Breneman.

The option can be exercised for a 90-day period at $17 a share.

The deal is subject to review by the Federal Home Loan Bank Board, which regulates federally chartered savings and loans.

Washington Homes owns 89 percent of the Washington Savings Bank.

It was not announced how many shares would be sold by each of the two officers. As of October 1986, Harnett owned 25.3 percent of the stock and Breneman owned 2.4 percent.

Neither executive could be reached for comment.

The announcement said Harnett and Breneman would continue to serve as executive officers and directors of Washington Homes.

Founded in 1965, Washington Homes builds residences in the Maryland and Virginia suburbs.

Announcement of the transaction Thursday sent Washington Homes stock to $10.75, up $1.63.

In trading on the New York Stock Exchange Friday, the stock closed at $12, up $1.50 for a two-day gain of 31 percent.

Scottish Heritable Trust is a publicly traded company based in York, England. It has U.S. investments in modular housing and textile manufacturing.