Private lawyers and the Montgomery County government have joined forces to maintain free legal help to the poor that will be lost through U.S. budget cuts.

Although legal aid organizations throughout the Washington area have been scrambling to prepare for what one D.C. director called "simply devastating" cuts in legal services, the effort is the area's first response to the problem.

The reductions will be caused by an $80 million cut in funding for the federal Legal Services Corporation, an organization that gives money to legal aid bureaus across the country.

In Montgomery County, the local legal aid office expects to lose $50,000 of its $135,000 budget through the federal cuts. This means losing one lawyer and two paralegal positions.

In a move that follows President Reagan's appeal to private enterprise and local governments to fill budget gaps, the Montgomery County Bar Association has pledged 80 hours of free legal service per week and county government will supply $23,000 to the office.

"We recognized that the poor in this county would be left without the ability to have legal services," said James J. Cromwell, president of the Montgomery County Bar Association. "We recognize this as our responsibility."

The need for legal aid is particularly pressing in Maryland, as the state last April discontinued its Judicare program, under which poor people could receive legal services from qualified lawyers.

Montgomery County Executive Charles Gilchrist agreed to spend $23,000 from the social services department fiscal 1982 budget after learning of the impending cut in legal services. "I agree with the bar association that it is unacceptable to deny poor people legal aid," Gilchrist said.

Other jurisdictions are facing similar problems. In some cases, legal aid bureaus already have shut their doors.

In the District of Columbia, the Neighborhood Legal Services Organization, the city's largest legal help organization, has had to close two of its seven offices because of a $457,000 loss of funds.

"It's made life for us very difficult," said Willie Cook Jr., executive director of the centers. "If you don't have this, poor people won't have any chance at all."

In Northern Virginia, the regional legal aid bureau is planning layoffs and seeking money from localities and social service organizations as officials acknowledge that services will shrink drastically.

"Even without the reductions, we only had the resources to handle 15 percent of the people (in Maryland) that were eligible for legal assistance," said Charles Dorsey, executive director for the Baltimore office of The Legal Aid Bureau, Inc, whose 12 offices throughout the state handled more than 77,000 cases and inquiries last year. "And in bad economic times, there are even greater demands for our services." Only the Montgomery County office, which handled 2,500 of those inquiries last year, has received help in easing the federal cuts, he said

The free legal help is available only to the poor.

In Maryland and Virginia, the income of a family of four must be $10,563 or less to qualify for free legal services, officials said. Linda Haspel, chief legal aid attorney for Montgomery County, cited one typical case where a Silver Spring woman with severe back problems and a $310 monthly welfare check was able to win previously denied Social Security disability benefits of $300 monthly through the free legal aid program.

Legal aid handles only civil cases, such as child custody, spouse abuse, and problems in public assistance, veterans or Social Security benefits.