Members of the D.C. City Council will get free parking spaces outside the District Building after all. Mayor Marion Barry decided the issue last night.

The mayor signed an order that authorizes the parking and clears the way for forgiving about $15,000 in past parking fees that several council members refused to pay.

Barry's order had the effect of reversing an unannounced veto by former mayor Walter E. Washington of a bill passed by the City Council on Dec. 12, granting itself the free parking and excusing itself from the $15,000 in fees.

The mayor's order said the council will not have to obey on order issued in 1973 by then-mayor Washington that all city employes must pay for parking on city-owned lots.

Members and top staff officials of the council park on a lot behind the District building that has 23 spaces. The mayor said that the council can have 15 of the spaces and that his appointees can have the other eight.

On two occasions, in 1976 and again last month, the council sought to excuse itself from the parking fees. The first effort was ruled legally defective.

Acting Corporation Council Louis P. Robbins urged the former mayor to veto the second bill on grounds that it sets a bad example for others. Former mayor Washington took that advice but avoided making an announcement when he left office Jan. 2.

Sam D. Starobin, city director of general services, said he would ask Robbins whether to try to collect the $15,000 in past fees. "My Don Quixote days are over," he said. Robbins told a reporter he was prepared to consider forgiving the payments.