The Alexandria City Council gave final approval yesterday to the winner of the city's first cable television franchise, despite a consultant's last-minute warning of a $662,000 error in the firm's budget figures.

In a 5-to-2 vote, council members gave the potentially highly lucrative franchise to Alexandria Cablevision Co. (ACC), headed by locally prominent investors.

The action makes Alexandria the second major Washington-area jurisdiction to grant a cable franchise. Arlington already has a cable system in operation.

The council went ahead with its decision despite a surprise announcement yesterday by its consultant, Lee A. Bertman, that "last-minute" analysis of figures submitted by ACC showed a $662,000 shortfall. The discrepancy might significantly affect subscribers' fees and the number of local programs the firm could offer, a city official said.

Some council members reacted with dismay to Bertman's statements. "How can grown men miss that much money?" Mayor Frank E. Mann asked Bertman. "Why are we finding these things out at the last minute? It's incredible."

ACC beat two competitors for the franchise - Alexandria Telecommunications Co. (ALTEC) and Alexcom Inc. - in a preliminary council vote last week, in part by promising extensive community-oriented programming.

In projections furnished the council before that vote, ACC said it planned to spend $1.45 million on local programs using revenues from subscribers' fees.

Bertman, a certified public accountant, told Mann and the council yesterday that his calculations showed the expected fee revenues would be $662,000 less than ACC was counting on. Bertman said that when he raised his concerns with ACC manager Douglas Jarvis, Jarvis denied the problem existed.

Bertman said that he discussed the subject again with Jarvis yesterday and that Jarvis acknowledged he had made a "computational error."

"We are at a point where (ACC's) budget is perhaps adequate, but there is not a tremendous margin for error," Bertman said.

The council killed a motion to go into closed session to discuss Bertman's information and defeated a second motion to delay the final vote until July, when a recently elected council will be in office.

"We can work this out later" through contract negotiations with ACC, which are scheduled for July, council member Donald C. Casey said. "Let's go with this."

Yesterday's vote came after other financial concerns were raised last week by Bertman and after charges by ALTEC and Alexcom that the city violated its own procedures by allowing ACC to modify its bid.

Citing "serious deficiencies" in ACC's original financial proposal, the Alexandria council demanded Tuesday, at Bertman's request, that ACC come up with $1 million in financing besides the $5.75 million it had raised already.

ACC executives yesterday gave proof that they had raised the extra $1 million, including $500,000 in cash, only to hear Bertman's statement moments later regarding the $662,000 shortfall.

ACC estimates that its service will cost individual subscribers about $17 monthly. If Bertman's figures are accurate, however, "either programs will be eliminated or the city will have to authorize a rate increase," according to Mary Sue Smoller, Alexandria cable administrator.

"Once a franchise is granted," Smoller said, "cities traditionally have little control over them."

Council members Casey and Robert L. Calhoun said that local control would be established through a performance contract that ACC will be required to sign with the city.

After the meeting Casey said Bertman was indecisive, and Bertman said that politics had been a factor in the council's desire to award the franchise.

A shouting match also erupted between former state Sen. Armistead Boothe, ALTEC board chairman, and veteran council member Nicholas A. Colasanto, who supported ACC.

"I knew the way you were going to vote right from the beginning," Boothe said. "It was your friends."

ACC's president is James Carroll, a former Alexndria councilman. ACC attorney James Thomson is a former Democratic state delegate from Alexandria.

Calhoun, Casey, Mann, Colasanto and Nora O. Lamborne voted for ACC yesterday. Voting no were Beverly Beidler and Ellen Pickering.