The British government today blocked plans for cheaper trans-Atlantic airfares this winter, stepping up a high-stakes legal battle with the U.S. government over whether American courts in some cases have jurisdiction over British airlines that fly to the United States.

The British Department of Transportation said that it was turning down all 17 applications -- 15 of them from U.S. airlines and two from British carriers -- for cut-rate fares because of the U.S. government's refusal to guarantee that British airlines would not face legal action under U.S. antitrust laws for unfair competition.

Britain's new budget airline, Virgin Atlantic, which was started in June and uses a single airplane, had objected to the proposed fares by the major airlines on the grounds that they were "predatory" and designed to force them out of business.

The stakes for Britain, however, go well beyond the fare proposal rejected today. They involve an important dispute between the U.S. and British governments over the whole question of "extra-territoriality," which Foreign Secretary Geoffrey Howe this week said "is a major concern for all of us in Europe. It runs counter to the important principle that national jurisdiction extends only as far as national territory."

They also involve the future of the state-run British Airways, one of the world's largest, which the British government plans to denationalize, or turn over to private investors through sale of stock, next year.

For the past few months, the U.S. Justice Department has been investigating allegations that British Airways and several other airlines conspired in 1982 to put Laker Airways, the maverick British carrier that pioneered cut-rate Atlantic fares, out of business.

British Airways has called such charges unfounded. And the British government questions the U.S. approach to such issues. But there is also concern within the government here that the investigation could hamper the sale of British Airways next year.

That sale will be among the biggest enterprises in the multi-billion-dollar shift of British industry into the private sector. Prime Minister Margaret Thatcher's conservative government believes the massive transfer will make the businesses more efficient and competitive.

Next week a team of lawyers and Department of Transportation officials will meet with U.S. Justice Department officials in Washington to discuss the progress of the investigation and to lay out the British view on such matters, especially involving international airlines.

The Justice Department investigation involves criminal allegations. However, there also is a billion-dollar civil antitrust case against 12 big airlines, including British Airways and the independent British Caledonian airline, being brought by the liquidators of Laker Airways in the United States.

The British government, sources here said, is especially interested in the Justice Department findings because if those allegations hold up, it would strengthen the civil case and perhaps even class-action cases in which passengers sue because they had to pay higher air fares.

Putting British Airways up for sale with potentially large, unresolved lawsuits could make that sale more difficult.

British officials argue that the critical dispute with the United States is over how to reconcile very restrictive language of U.S. antitrust laws with the fact that major international airlines that operate under an air services agreement, as do U.S. and British carriers, must have some "normal, respectable" discussions to agree on fares to present to their governments.

The British officials said they are not defending discussions between airlines aimed at putting anyone out of business. But even if that were the case, one official said, U.S. court actions still are not proper if the discussions took place in Britain. In this view, "the principle of extra-territoriality means that U.S. courts should not be touching things that happened in Britain."

In announcing today's decision not to allow requested reductions in fares to about $310 round-trip, British officials said they were acting "reluctantly" and held out hope that the rejection might be rescinded.

Deputy Transport Minister Michael Spicer said, "I am naturally very disappointed at the lack of response from the U.S. government as it deprives travelers of the benefit of these lower fares. I hope, however, that the necessary reassurances will be forthcoming shortly, at which time the airlines will be free to refile their proposals."