Construction has begun on the Frank E. Basil Inc. world headquarters building at McCormick Properties' Inglewood business community at Landover.

The headquarters for the international architectural, engineering, design and construction services firm will be six stories and contain approximately 90,000 square feet of space. The building will accommodate about 400 employes and is the first of three Basil structures scheduled for construction at Inglewood during the next seven years.

McCormick, a subsidiary of Baltimore's McCormick & Co. Inc., has designed and is building the multimillion dollar Basil headquarters, but the Basil company will probably purchase the building once it is completed, according to a McCormick spokesman. Completion of the project is scheduled for late 1983.

McCormick began developing the Inglewood business community a year and a half ago and approximately a quarter of the 230-acre site has been prepared for construction.

Last spring, archeological experts from the Smithsonian Institution and the University of Maryland identified bones from ancient mammoths uncovered at the site during preliminary excavations.

Inglewood is based on McCormick's successful corporate headquarters model complex in Hunt Valley, Md. Company officials plan to duplicate Hunt Valley's off-street parking, tree and grass areas and controlled maintenance.

The Basil headquarters is the second building under construction at Inglewood. The first building, Tech Center I, is one of two McCormick buildings planned for the site. Tech Center I has five stories with 52,000 square feet of space. McCormick will use part of Tech Center I for office space and lease the remaining space. Construction is scheduled for completion in early 1983.

McCormick will start on its second building once leasing for Tech Center I is complete. Plans for other buildings will be developed as the demand develops.

Further plans for Inglewood include a 200-room hotel.

McCormick Properties also developed the Rutherford Business Center at the site of the old Rutherford Airport near Baltimore.

Other recent developments in commercial leasing in the Washington metropolitan area:

* Wilmot, Bower & Associates, an architectural and engineering firm specializing in medical facilities, has leased 30,400 square feet of space at 1350 Piccard Drive in Rockville. The company is moving its newly created corporate heaquarters to the building. The five-year lease has an aggregate rental value of $1.9 million.

* Prudential Insurance Co. has leased 6,000 square feet of space at the Montgomery Executive Center in Gaithersburg. The company is moving its sales office to the building. The five-year lease has an aggregate rental value of $400,000.

* Gray Drug Fair is relocating most of its operations at 6295 Edsall Road at the intersection of I-395 in Alexandria to its parent company headquarters in Cleveland. Gray Drug will retain a minimum of 5,000 square feet of the building's total 71,000 square feet.

Weaver Bros. Inc.'s commercial leasing division is seeking tenants to lease 20,000 square feet or more. Any tenant who leases more than 40,000 square feet of the building may replace the facility's Gray Drug Fair corporate identity with that of their own firm.

* Quality Leasing, a car rental agency, has established its headquarters in the Executive Plaza Office Building in Springfield. Ryan Financial Services has leased an additional 430 square feet of space in the same building.

* United Mortgage has located its headquarters at the Gould Building at Route 450 and the Capital Beltway.

* Priest Bridge Station, a 10,000-square-foot office and retail business facility, is now under construction at Route 450 and Priest Bridge Drive in the Priest Bridge Business Park in Crofton. Occupancy is planned for spring of next year.

The one-story building was designed and is being built by Gardiner & Gardiner Inc. of Crofton and will feature a brick colonial-style exterior with a slate canopy roof.

The project is the first phase of a planned 30,000-square-foot office and retail complex at the 65-acre site. Financing is by Annapolis Banking and Trust Co.