Cambridge will remove all asbestos insulation from city schools this summer regardless of whether or not the state legislature approves a pending bill allocating money to help defray the costs, city officials said Friday.

"We're going to get on with lightning speed," said Mayor Alfred E. Vellucci, who chairs the Cambridge School Committee. He added that the city had started the clean up program last year.

The school committee voted last Tuesday to require that the insulant be removed from schools by September 1, 1983, said School Committee Member Jane Sullivan.

Workers have already encapsulated all asbestos, and the city's school department plans to spend approximately $85,000 this summer to remove the insulant, said Oliver Brown, assistant superintendent for planning and management.

Asbestos, commonly used through the 1960s for building insulation, has been identifies as the cause of two forms of caner and lung disease.

One week ago, the state Department of Education estimated it would cost over $25 million to clean up schools throughout Massachusetts, and a bill has been introduced by Sen. Chester G. Atkins, chairman of the Senate ways and means committee, to raise $15 million t help cover the cost.

Cambridge began to deal with the asbestos problem before recent publicity said Brown. "We took the initiative last fall to take air and solid tests," he explained.

He added that since then, the city had established permanent files on the problem, tested all public school areas, and notified parents of the asbestos risk.

The city's action to remove asbestos has apparently satisfied parents said Sullivan, adding that she had received very few calls on the issue.

Brown said Cambridge has been motivated to eliminate asbestos entirely because of the uncertainly over the danger it poses.

"Eventually the standard will be to get rid of it all," he said, adding that "nobody knows what they're talking about" when it comes to the carcinogen.

According to legislative observers, the chances are good that Cambridge will be reimbursed to some extent for its cleanup.

"I would think the mood in the legislature is that hazardous waste and asbestos are problems which need to be dealt with acutely," said Jeremy Eden, legislative assistant to State Sen. John W. Olver (D-Buckland), chairman of the taxation committee.

He added that Atkins's and bill was almost assured of passage, although he said its future was less certain in the State House.