The Reagan administration and the House have agreed to a compromise on 1982 food-stamp spending that would eliminate the need for an across-the-board cut in benefits this winter, Rep. Frederick W. Richmond (D-N.Y.) said yesterday. He heads the Agriculture subcommittee responsible for food stamps.

The compromise, worked out with Office of Management and Budget Director David A. Stockman and bipartisan backing, means the House accepts an extra $700 million cut in spending in exchange for a higher spending ceiling than the administration wanted, $11.3 billion. The $700 million savings is to be achieved by delaying a scheduled cost-of-living rise in the benefits for six months.

The deal removes a major obstacle to House action on the comprehensive farm bill.

The adjustments come on top of some $1.8 billion in food-stamp cuts already approved by Congress at President Reagan's request this summer. Effective yesterday, they knocked 1 million people off the rolls and reduced benefits for millions more.

The House finally approved a bill to block that million-dollar-a-day price-support increase for dairy farmers, but the action was foiled once again in the Senate by dairy state Sen. William Proxmire (D-Wis.).

The delay means that the higher subsidies, triggered when the fiscal year and the farm law died at midnight Wednesday, will be in effect at least until some time next week.

Dairy price supports have been a prime administration target for budget cuts. Moreover, retailers may use the temporary increase as an excuse to raise milk prices to consumers permanently, Agriculture official Don Friedly said.

The new farm bill eventually will resolve the issue for four years. Earlier House and Senate stopgap measures to block the rise were foiled by Proxmire and others.

Although the new farm bill is expected to return dairy supports to existing levels, the failure of Congress to enact it before the fiscal new year triggered a 1949 law that boosts the subsidy from $13.10 to $13.56 per 100 pounds of raw milk and could cost the government up to $10 million a week more than it would otherwise have paid.

An $8.6 million national tourism bill was passed by the House, 288 to 112, and now goes to Reagan, who might veto it.

The measure, which would upgrade the federal role in the tourism industry, authorizes a new agency, replacing an old one, in the Commerce Department to develop a detailed plan to encourage travel to the United States.

But the funding is higher than the administration had indicated it would accept, and one insider said there is a chance of a veto.

Although international travel receipts here are growing at about 16 percent a year, President William D. Toohey of the Travel Industry Association of America said in urging House approval that the industry "is losing pace in the international arena due to an intolerable marketing disadvantage for lack of a defined federal role."

Leading the opposition, Rep. William E. Dannemeyer (R-Calif.) argued that the measure "should not be supported at a time when we are asking those much less well off than the tourism industry to absorb additional budget cuts."

In what has become an annual rite of the fiscal new year, Sen. Edward Zorinsky (D-Neb.) returned a chunk of cash to the Treasury. This year, the gift amounted to over $361,000 that he saved by not hiring as many office aides as he could have. And he said he also will return almost half of his $51,000 annual office expense fund. A former mayor of Omaha, he has given back more than $1.6 million since he took office in 1977.