One battle set off by President Reagan's budget-cutting crusade will soon reach the breakfast tables of every family in America: the coming fight over federal supports for the price of milk.

The new administration has made a still-unannounced decision to try to prevent a scheduled increase in milk price suppports. This, if congress concurs, would save milk drinkers about 15 cents a gallon beginning April 1. Powerful dairy interests will fight this effort with all the political influence that $1.2 million in campaign contributions (in 1980 alone) can buy.

The effort to skip the scheduled April 1 increase in milk prices will start a political struggle likely to continue for most of this year. At stake for the nation's dairy farmers are subsidies that this year will total $2 billion from the federal treasury.

This will be a battle over a venerable deal between government and dairy farmers. The deal is this: in return for an assured supply of milk, butter and cheese, the government abolished the free market in milk.

The nation's dairy farmers are guaranteed a market for their product and a living wage for their long hours of hard work, and every major city is assured a local supply of milk to drink. But Adam Smith would cringe. Free enterprise has been eliminated from the dairy farming industry.

Apparently, Reagan cringes, too. His administration has decided to try to reduce the large and accelerating cost of the dairy price-support program.

But the dairy interests will fight to protect their longstanding deals with the government. They are prepared to agree that $2 billion in price supports is too much, but not a lot too much.

Dairy farmers will call on their friends in Congress too protect their interests, and they have a great many friends. In 1980 the three largest dairy cooperatives gave more than $1.2 million to candidates for the House and Senate. This made them one of the most generous special-interest groups in the country.

Historically the United States has enjoyed abundant supplies of milk and dairy products at reasonable prices. Even the dramatic recent increases in milk prices have not changed that fact. In Canada yesterday, for example, a half-gallon of whole milk in a Toronto supermarket would have cost $2.20; in Washington it was about $1.15.

The American milk market is an elaborate maze of market areas, milk sheds and government marketing orders establishing prices at which the Commodity Credit Corp. of the Department of Agriculture will purchase butter, American cheese and powdered nonfat dry milk.

The basic price is set by Congress and expressed as a percentage of "parity." Parity is a price for milk based on market conditions in the 1910/14 period, a particularly good time for dairy farmers.

The system is complicated by the fact that, under federal milk marketing orders, the price of milk also rises steadily the farther it is produced from the Wisconsin-Minnesota area in which milk can be produced most efficiently. Therefore, milk sells for a lot less in Milwaukee than it does in Miami.

Under the basic milk price-support law passed in 1949, the secretary of agriculture is empowered to set the support price at 75 to 90 percent of parity, basing his decision on market conditions.

However, in 1977, milk producers persuaded Congress to enact temporary legislation reguiring that the level be pegged at 80 percent of parity or above until the end of September of this year. The 1977 law also required that the parity level be adjusted for inflation twice a year instead of once, as it had been previously.

In the last few years these new terms have produced huge new milk surpluses -- the higher price, the more farmers produce -- and burgeoning costs to the treasury.

Milk supports cost $230 million in fiscal 1979, and could be more than $2 billion this year. The Commodity Credit Corp. is sitting on mountains of butter, cheese and dried milk. In fiscal 1981, the CCC will purchase 275 million pounds of cheese and 600 million pounds of dried milk.

The government currently has outlets that will use up about half of these surpluses; the rest will sit in warehouses leased by Uncle Sam.

Agriculture Department officials say they are not sure why they are suddenly buying so much dairy products. Clearly, dairy farmers find the current price support level attractive, and are happy to sell as much as they can produce at today's price levels.

But some officials also think that Americans have switched off milk products in unprecedented numbers. One theory is that the rising prices of dairy products have caused a sharp reduction in demand for them. The government admits that its statistics are insufficiently precise to explain just what has happened.

The Reagan administration's first attempt to save money on dairy price supports will be modest. If it can win congressional approval for a bill eliminating the April adjustment in the parity level, that could save $125 million to $135 million this year.

On Sept. 30, the law mandating a price support at 80 percent of parity will expire, and the support can fall back to 75 percent. This change will lower the price at which the government buys milk, and presumably will discourage farmers from producing as much as they do now. But the precise level of potential savings to the treasury is difficlut to predict.

However, none of this will happen automatically. The dairy lobby, one of Washington's most effective, has a plan of its own: to leave the April 1 parity adjustment in place, and then to replace the law expiring in September with a measure that would allow parity levels to fall when surpluses accumulate, but would also bring them back to 80 percent or higher when surpluses start to fall.The net savings to the treasury from this plan could be significantly smaller than from the administration's apparent plan.

The word "apparent" is apt, because the administration has considered trying to reduce the parity level to 70 percent. A reduction that greatly could alter the dairy industry dramatically, while probably eliminating significant federal price supports.

Even with price supports at 75 percent parity, the government has not had to make big milk purchases in some recent years -- years when demand for milk products exceeded supply, pushing market prices above the government-supported level.

Patrick Healy, Washington representative of the National Milk Producers Federation, will lead the lobbying efforts of the major milk cooperatives, which represent more than 80 percent of the country's dairy farmers.

Healy is a master of apparent reasonableness. For example, he volunteers that the price support level is too high, and he is drawing up a plan that would involve some reduction. But not too much.

Healy contends that the April 1 parity adjustment is good for both the industry and consumers, because it has the effect of cushioning the impact of inflation-caused increases in the price of milk. Better to let it come into effect slowly, in two stages, Healy argues.

Healy will be up against the administration, Common Cause, various consumers' groups and big commercial users of milk. Last week in Washington, Richard T. O'Connell of the Chocolate Manufacturers Association convened a meeting of milk users, and proposed that a number of firms and associations chip in $7,500 each to hire a lobbyist.

He proposed John A. Knebel of the firm of Baker & McKenzie, the same John A. Knebel who took over from Earl L. Butz as secretary of Agriculture in the waning days of the Ford administration, when Butz was forced to resign.

Whether Knebel is retained remains to be decided but there is no question that firms such as Sara Lee and Pizza Hut, both of which use huge quantities of dairy products, and trade associations representing candy makers, restaurants and others will be active participants in the coming fray. An old-fashioned Washington donnybrook seems guaranteed.