A House Judiciary subcommittee and 10 Democratic senators have asked the General Accounting Office to investigate the unprecedented consulting fees collected by President Reagan's appointees to the board of the Legal Services Corp.

The legislators also asked the GAO to look into government-paid fringe benefits, including membership in the private club of his choice, in the contract of Donald Bogard, the new Legal Services president.

Meanwhile, responding to controversy over finances at Legal Services, the government-funded program to provide legal assistance to the poor, Congress has approved language to restrict severely the consulting fees and benefits for the board or its president. The language, in emergency funding legislation for most government agencies, would prohibit payment of taxpayers' money for membership in private clubs, and would forbid the special severance agreement in Bogard's contract that provides one year's salary as well as expenses and benefits.

The amendment would restrict Bogard to the same severance arrangement as those of other federal employes. A spokesman at the Office of Personnel Management said federal workers in their first 10 years of service are entitled to a year's severance pay for each year worked.

Bogard, who started his job Dec. 12 at a salary of $57,500, would be entitled now to a little less than $29, his hourly rate of pay, if he is fired.

The amendment also would limit board members' consulting fees to time spent at official meetings. Corporation documents show the board collected $156,000 in consulting fees in the first 11 months of 1982, more than twice the level of any previous board.

In other congressional action yesterday, the House Wednesday Group, a coalition of moderate Republicans, sent Reagan a letter signed by 31 House members and four senators, all Republicans, reminding him that Congress has mandated the "continued operation" of the Legal Services program and asking that his future nominations to the board be "outstanding attorneys committed to the fair and effective legal representation of the poor . . . . "

Meanwhile, the GAO was asked over the weekend for an investigation of "possible improprieties," including whether it was proper for the 11 board members to receive any fees. The House subcommittee request was bipartisan, signed by all seven on the subcommittee.

One issue to be investigated will be whether board members, recess appointees never confirmed by the Senate, are entitled to any compensation. The law provides that in most cases recess appointees may not be paid for services if they were appointed to fill a vacancy which existed while the Senate was in session.