The D.C. City Council yesterday voted overwhelmingly to offset federally mandated cuts in welfare benefits for working-poor families in Washington by giving them more to pay their heating and utility bills, increasing their food stamp allotments and offering them free health care if they no longer qualify for Medicaid.

With the adoption of this $2.5 million compromise plan, drafted by Mayor Marion Barry, the D.C. government apparently will become the first jurisdiction to compensate welfare clients for the loss of federal benefits through Reagan administration budget cuts, according to city and federal officials.

Working-poor families earning up to$1,200 a month currently qualify for between $89 and $186 a month in Aid to Families with Dependent Children (AFDC).

Under stringent new Reagan administration policy and spending guidelines, about 2,500 of the 3,800 working-poor families would be dropped from the AFDC rolls in January. The rest would receive reduced benefits.

After yesterday's council meeting, Barry pledged that, under his plan, none of those families would suffer a reduction in their overall level of assistance. Nor would there be an interruption in payments, while the new program is set in motion, he said.

The mayor acknowledged, however, that there is not enough money in the current budget to pay for the program and that he must seek supplemental authority from Congress next year to raise and spend the additional funds.

If Congress does not grant the financially strapped city government the additional spending authority, Barry said he would reduce spending in other areas of the budget for the D.C. Department of Human Services.

The council yesterday also approved an emergency measure to avert a projected $26.1 million deficit in the city's unemployment compensation trust fund next year without borrowing from the U.S. Treasury.

To accomplish this, the council voted to increase the wage base used in computing the employers' contribution. Employers currently pay unemployment taxes on the first $6,000 of an employe's wages. The new provision would make taxes payable on the first $7,500. At the same time, the council decided to limit a scheduled increase in the maximum weekly benefits for the unemployed workers from $222 to $206.

Even with these and other changes, the trust fund still would end the fiscal year next Sept. 30 with a $5.3 million deficit -- adding to a $51.5 million long-term deficit that has been piling up since 1975.

Council member John A. Wilson (D-Ward 2), criticized the Committee on Housing and Ecnomic Development for being too accommodating with business and labor groups, which had resisted Mayor Barry's plan to increase the taxable wage base to $8,000 and reduce the maximum benefit to $198 a week.

"I will not vote for anything that leaves this fund with a deficit," said Wilson, chairman of the Council's Finance and Revenue Committee.

Council member Charlene D. Jarvis (D-Ward 4), chairman of the housing and economic committee, which had jurisdiction over the bill, said the measure was a reasonable compromise that would give the city time to consider long-term solutions to the problem of the trust fund's insolvency.

Council member Jerry A. Moore Jr. (R-at Large), said that the compromise measure was fair to both business and labor, "providing a reasonable balance that helps each one to survive" during the recession.

The Greater Washington Central Labor Council, the city's largest umbrella labor organization, said that the council-approved plan would put "the city's fiscal woes on the backs of unemployed workers."

"This proposal is hasty and we regret the city felt compelled to take this action," said Robert E. Petersen, president of the labor council. "The administration bears the responsibility for forcing the city into this heartless position."

The plan approved yesterday to maintain current levels of assistance for working poor families supplanted a measure, tentatively approved by the council on Nov. 24, to spend $5 million during the current fiscal year to maintain the present level of AFDC benefits.

Barry claimed the council plan, introduced by David A. Clarke (D-Ward 1), was unworkable and seemingly flouted Reagan's edicts to reduce overall AFDC benefits for working-poor families and could jeopardize all welfare benefits for those recipients.

Barry insists that his indirect approach to helping the working poor would not conflict with Reagan's new guidelines, since energy assistance is not counted as income in determining a family's eligibility for AFDC, food stamps and Medicaid.

The U.S. Department of Health and Human Services (HHS) declined to comment on the council's action yesterday until it sees details of the council's program.