The United Mine Workers of America has agreed to sell its controlling interest in The National Bank of Washington for $70 million to a group of New York and Washington investors, including the bank's senior officers.

The agreement in principal to sell Washington's oldest and third-largest bank, acquired by the mine workers during the 1940s when the union was at the height of its powers, was announced late yesterday by the union and bank officials. A final agreement is subject to completion of financing arrangements and the necessary approvals by regulatory authorities.

Details of the preliminary agreement were not announced, but officials said management of the bank and its holding company, Washington Bancorp, will remain intact after the sale. Luther H. Hodges Jr., chairman and chief executive officer of the bank and its holding company, confirmed yesterday that he has agreed to join the investor group, which is headed by Peter Del Col and Roy B. Simpson, partners in Colson Inc., an independent New York investment company.

Simpson and Del Col, who is a former principal in Bradford Securities, have organized Colson Inc. as a holding company which would acquire Washington Bancorp, presumably as a preliminary step to a merger of Colson and Washington Bancorp.

The investor group also includes C. James Nelson, president of NBW and Washington Bancorp, and other members of the bank's senior management who were not identified. The investor group may eventually include two foreign groups. The foreign investors, said to be a British pension fund, and an American-owned firm in England, would hold minority positions in the new company, which was organized to buy the bank, Hodges said.

Hodges said the main task to be accomplished now is to put together the financing for the deal in which the UMW has agreed to sell its 76 percent interest in the bank for about $66 a share. The book value of Washington Bancorp at the end of 1984 was $51.54 a share.

Although Colson Inc. will act as agent and buyer of the UMW stock, Hodges said he will coordinate an effort here to obtain part of the financing.

"I am interested in a broad investment by additional investors in the Washington community," Hodges said in an interview yesterday. "I have committed to invest in the new holding company but a lot of it depends on the nature of the response" from other investors in the Washington area

Hodges added that even though he will be a principal in the investor group, it is too early say what percentage of the stock he will own.

Banking industry sources reported two weeks ago that a group of investors from New York appeared to have the inside track in coming to terms with the mine workers union. The group was not identified at the time, however.

The UMW has been the bank's major stockholder since the 1940s, when the union's founder John L. Lewis bought controlling interest. The mine workers' executive board authorized union President Richard L. Trumka and other officers to sell the bank several months ago, but the group had been unsuccessful until now in finding a buyer willing to pay what it considered a fair price for a bank of its size in this market.

Trumka, who described yesterday's agreement as "a positive step in making the UMWA financially secure for years to come," said the dividend income that the union received from its investment in NBW has been "significantly less," on a percentage basis, than members of the union receive on their personal savings accounts. By freeing the union's holdings in the bank for other investments, he added, "we will be able to earn at least seven times our current return."

Interest in buying NBW has accelerated in recent months, particularly in the wake of improving financial results. Under Hodges' leadership, NBW has recovered from a string of earnings losses and adverse publicity resulting from a series of questionable loans. Those loans and other activities prompted federal regulators to order changes in the bank's operation and leadership in 1980.

Washington Bancorp recently reported a 34 percent increase in profits, to $8.2 million in 1984.