The Alexandria City Council decided last night that despite the displeasure of some West End residents over plans to construct a high-rise apartment building in their neighborhood, it had no legal way to stop it.

Councilwoman Margaret B. Inman, a Republican, had asked council to reconsider building approval of the proposed 206-unit building at N. Beauregard and N. Armistead Streets, saying neighborhood residents had not been given enough notice of the planned construction, which is scheduled to begin later this year. Inman noted that the site plan for the building had been approved nine years ago when many current area residents did not live there. " [The procedure] has, in effect, put something over on the citizens," she said. "Council would be derelict if we did not take a look at it and allow the people to take another look at it."

The planned high-rise upset a number of nearby condominium dwellers who say its construction will drain public facilities in the area and create new traffic congestion.

Neighborhood residents said they also were angry about the fact that they first became aware of the new building only last November after newspaper reports that the council had voted to issue $20 million in tax exempt bonds for its construction.

City Attorney Cyril D. Calley advised council members last night that they could not reconsider the site plan without the possibility of becoming liable for expenses already incurred by the developer, Midlands Investments Inc. of Bethesda.

Angus Olson, executive director of the Alexandria Redevelopment and Housing Authority, which will issue the bonds, told the council last night he had complied with all legal requirements to give neighbors notice of the building's construction.

The council, however, did request its staff to bring together the developer and residents to discuss the problems they envision.

"The letter of the law was met but I think we have not got anywhere near the spirit of the law," said John Fulton, one of the unhappy neighbors. "The issue is not dead as far as we are concerned."

The apartment complex is scheduled for completion in 1986.