President Reagan's budget-cutting plans passed their first full test in Congress yesterday as the House, by voice vote, concurred with the Senate in approving his proposal to kill an April 1 increase in milk price supports.

It was a pleasing victory for the White House, which had chosen a hard-line approach in Congress on this early issue. All hints of compromise were rejected as the new administration demanded, and got, a total victory over the dairy lobby, traditionally one of the most effective in Washington.

The House was thought to be more friendly than the Senate to dairy farmers. The Senate had approved the administration bill to skip the scheduled increase in the milk price support 88 to 5 on Wednesday.

But pro-dairy representative clearly saw that they would lose big if they forced a roll call in the House, so they ducked one, allowing the measure to be approved yesterday on a voice vote.

House Republicans hailed the vote as a triumph for the president, but it was far from the hardest fight Reagan is expected to face in his effort to force reductions in government expenditures.

In fact, the cost-cutting move approved yesterday was one that President Carter had also proposed, and which important elements of the dairy industry realized would probably be approved no matter who won last November.

The current milk price support is $13.10 per hundredweight, and it would have risen to $14 under the dairy legislation now in effect. The bill approved yesterday amends that legislation.

The federal government is now sitting on more than a billion pounds of powdered dry milk, cheese and butter, while farmers continue to produce the stuff at a fast clip.

Under the federal milk program, the government will buy any surpluses not sold on the open market, a fact that allows dairy farmers to maximize production without concern for conventional demand in the marketplace. This year the milk-support program will cost the Treasury about $2 billion.

The bill approved yesterday would reduce the program's cost by about $147 million, according to administration estimates. By holding down the price of milk, however, it would also save consumers hundred of millions of dollars in the next six months. Had the bill not been passed, the retail price of a gallon of milk would have risen from 10 to 15 cents.

The National Milk Producers Federation saw yesterday's vote coming months ago, and began preparing fallback positions. Dairy lobbyists have proposed a new milk-support scheme that would allow for a sliding scale of price supports depending on the amount of government surpluses on hand. According to this formula, it was proper to skip the scheduled April 1 increase because surpluses are currently so high.

The dairy lobby had hoped to work out an agreement with the new secretary of agriculture, John R. Block, to adopt this proposed sliding scale as part of the general revision of farm legislation that must be enacted by Oct. 1.

A little reasonableness now should be rewarded with a cooperative attitude later, dairy lobbyists reasoned. But Block refused to play, declining even to give an outline of the dairy program he will propose in the new farm bill, despite demands from some members of the House that he do so.

In the end even staunch dairy industry allies in the House Agriculture Committee rolled over for this budget-cutting maneuver, not least because Speaker Thomas P. (Tip) O'neill Jr. (D-Mass.) told them to.

"We have to be responsive to the mandate of the American people," explained E. (Kika) de la Garza (D-Tex.), chairman of the Agriculture Committee. He said those words on the House floor yesterday, but by the look of him his heart wasn't in them.