The House yesterday approved a $56 billion appropriation for the Department of Housing and Urban Development and several other agencies that continues many programs President Reagan wanted to scale back or eliminate, but still freezes total spending for next year at current levels.

The 340-to-73 vote in favor of the measure for fiscal year 1986 occurred after the House voted down increases in public housing programs put in the bill by the House Appropriations Committee.

The HUD bill was the fifth appropriation measure taken up by the House since House-Senate negotiations over a 1986 budget resolution stalled. Usually the chambers work out a compromise budget resolution setting overall spending targets before taking up individual appropriations bills.

Negotiations have foundered primarily on the issue of domestic spending cuts. Frustrated by the stalemate, the House on Wednesday voted to put its own budget into effect unless a budget agreement with the Senate is reached.

The HUD bill, like the other appropriations measures adopted so far, is within the spending limits set in the House-approved budget resolution. The measure provides about $9 billion more than Reagan requested and is about $2.5 billion below the 1985 funding level.

Programs that Reagan wanted to terminate that were funded in the bill include Urban Development Action Grants (UDAG) used by many cities to revitalize depressed areas, rehabilitation loans used to help urban homesteading in many areas and general revenue sharing with local governments.

The bill approved by the House continues the UDAG program but cuts its funding by 25 percent. It reduces revenue sharing funds by about the same amount.

The bill also includes funding for the Solar Energy and Energy Conservation Bank, Indian housing and housing for the elderly and handicapped, three programs for which Reagan requested no money in his 1986 budget proposal.

Reagan had proposed a two-year freeze on all subsidized housing programs, which the House refused to accept, instead approving about $9 billion for those programs. Funding for subsidized housing has shrunk dramatically since Reagan took office, from about $25 billion in 1981 to just over $10 billion this year.

Most of yesterday's eight-hour debate on the bill revolved around funding for low-income housing. The appropriations committee had put $1.98 billion in the bill for 10,000 new public housing units, about 5,100 more than this year's level and 10,000 above Reagan's budget request.

But the House voted 236-to-172 in favor of an amendment eliminating the committee-proposed increase and instead froze the number of units at the current level.

Supporters of the amendment, led by Rep. Steve Bartlett (R-Tex.), argued that the House-approved budget freeze should apply to individual programs and not just to a total figure for the HUD package. Opponents said it was a "brutal" cut that would only hurt the most needy.

The House accepted another Bartlett amendment that cut $500 million from the bill for unspecified new housing programs.

Lawmakers rejected a third amendment by Bartlett that would have reduced all assisted housing funds by 2.5 percent.