The Alexandria School Board voted last night to ask the City Council for an additional $770,000 to build a controversial high school rowing facility on the downtown Potomac River waterfront.

The City Council begrudgingly set aside $954,000 last May for the boathouse for 200 oarsmen from T.C. Williams High School. Council member Donald C. Casey argued at the time that the 2 1/2-story building was too expensive and might destroy the "open space on the waterfront."

When told of the new estimate last night, Casey said, "We dislike surprises like this very much." The additional funding, he said, would have to be pried from some other part of the city budget. Rather than do that, he suggested that the specially designed 17,000-square-foot building be scaled back.

School Superintendent Robert W. Peebles attributed the cost increase, "which was hard to swallow," to soft soil near the waterfront that will require more expensive steel supports than originally thought.

The T.C. Williams crew now uses a cinder-block boathouse behind the Torpedo Factory on Cameron Street. The city plans to knock down that facility to make way for a restaurant and specialty shops as part of its extensive waterfront development. The new facility at the foot of Madison Street in Oronoco Bay Park is scheduled to be completed in the spring of 1986.

Mayor Charles E. Beatley said when queried last night that even though the rowing facility, which is designed to blend into Old Town's federal architecture, now would cost more than $1.7 million, "it's worth it to the city."

The revenue and jobs generated by the new restaurant and shops will offset the high cost of relocating the crew facility, he said. Both Beatley and City Manager Doug Harman said the facility is part of the city's "culture" and would benefit more than just the 200 students who would use it.

School Board Chairman Lou Cook will present the increased budget request to the Council on Dec. 11. She said she is not expecting a warm reception: "The council has gone on record favoring the new crew facility. It's now time for them to bite the bullet. I just hope they don't use it on me."