W.R. Berkley Corp. of New York, a holding company for insurance businesses located primarily in the Midwest and southwestern states, last week announced plans to acquire one of Washington's oldest enterprises--Firemen's Insurance Co., chartered by Congress in 1837.

Under an agreement approved by executives of both companies, Berkley will offer to buy all shares of Firemen's for $120 apiece, a purchase price of about $6 million. The acquisition must be approved by regulatory officials and by the approximately 200 stockholders of Firemen's at a meeting set for March 30.

Berkley Chairman William Berkley and Firemen's Chairman Herbert Pasewalk said the New York concern has been granted an irrevocable proxy in favor of the deal by owners of 42 percent of Firemen's shares. Berkley also received an option on these shares at $120 each if the merger is not consummated, provided that Berkley makes the same offer to other owners.

Firemen's, with assets of about $9 million, mostly offers fire and homeowners insurance in the District, Maryland and Virginia. The relatively small D.C. company long has been profitable; earnings rose from $324,000 ($10.46 a share) in 1979 to $550,000 ($13.25) in 1980. Premium volume in 1980 was about $5 million.

Berkley has assets of about $200 million. Both companies are traded publicly in the over-the-counter market.