Freddie Laker is making trouble again - trouble for other airlines and trouble for the British government.

The exuberant chairman of Britain's Laker Airways, which started a revolutionary low-cost, no-reservations and, so far, very successful air service between New York and London three months ago, recently applied for a license to initiate the same type of service to Los Angeles.

Laker has proposed that the nonstop service begin in September, 1978, the first anniversary of the Skytrain flight linking New York and London. The roundtrip ticket price for the proposed service would be $456, less than half the current roundtrip fare of $970 charged by Trans World Airlines and British Airways, the two carriers currently flying between London and Los Angeles.

But there's one problem. Britist Caledonian Airways, a British carrier with an extensive route system in Europe, Africa and South America that recently began flying between Houston and London, once flew scheduled flights between London and Los Angeles and claims it has prior rights to the route.

Only one of them - Laker or B. Cal, as it's called in Britain - can be allowed to fly the route. Under the terms of an agreement signed this year governing air services between the United States and Britain - an agreement the British sought - each country has the right to designate two routes to be served by two of its carriers. (All other routes between the two nations can by one one airline from each country.)

If Britain choses the Los Angeles-London route as one of its options (New York has already been designated by the British as one of its two routes), it has only airlines slot left to fill since British Airways was already designated by the government as a carrier to Los Ageles. No route may ever get three of a country's airlines, under the terms of the agreement.

"If Laker wants a scrap, they have got one - every step of the way to the highest legal authority in the land if necessary," Ian Ritchie, B. Cal's external affairs director, vowed two weeks ago.

British Caledonian has a license from the British Civil Aviation Authority. It had, as well - until recently - the British government's designation for the London-Los Angeles route. (A carrier needs both a license from its government's aviation authority as well as the government's formal designation for the route before it may being service.) B. Cal was in fact operating scheduled service between London's Gatwick Airport - the same airport Laker uses - and Los Angeles for 18 months until end of September, 1974, when it suspended service "temporarily" because of the fuel crisis and the worldwide recession.

"But at the time, we said we would recommence the service as soon as feasible," a B. Cal spokesman insists.

When it wanted to restart service, however, in the 1975-76 period, it ran up against Britain's civil aviation review, according to B. Cal, officials. Then, during the 1976-77 period, when the United States and Britain were negotiating the new agreement, airlines in Britain were prevented from making any U.S. route changes.

Now, although B. Cal still holds a CAA license to operate the London-Los Angeles route, it cannot start up service again until the British government formally designates it anew on that route.

Under the Bermuda II bilateral, as the agreement between Britain and the United States is called, each country was to redesignate by Nov. 1, 1977, the routes and carriers that were to be ongoing. The British government did not redesignate B. Cal on three routes for which it already held a license, Los Angeles, New York and Chicago.

"We made it clear to the British government we wanted to go back to L.A.," Leonard N. Bebchick, B. Cal's joint company secretary and counsel, says. "Our license was never revoked, and we wanted the designation, but the British government sat on that request. Now, along comers Laker..."

"It's going to be real scrap," he predicts, before the CAA and perhaps on the political front with the government as well. "And we'll go to court if we have to," he says.

B.Cal has said that, if it is permitted to reintroduce service between London and Los Angeles, it will offer a full-spectrum service, including low cost budget and standby fares.

Ironically, B.Cal finds itself in something like the same position Laker was vis-a-vis the British government not so long ago - fighting it, license in hand.

Laker had been granted a license as a scheduled foreign air carrier by the British CAA in 1972, and in 1973 was formally designated by the British government to operate the London-New York route. Then, during the much-delayed processing of Laker's application on this side of the Atlantic - by the Civil Aeronautics Board - the British government took action that had the effect of precluding Laker's proposed Skytrain operations under its license indefinitely.

The British government set a policy that essentially divided the world into spheres of influence for the two British airlines already operating under the British Civil Aviation Act. On inter-continental routes, the new policy allowed no point-to-point competition between British carriers.

Since British Airways already flew into New York, Laker was frozen out, and the government said it wouldn't allow Laker to be an exception to its general policy. The CAA was asked to take action to revoke Laker's license.

Laker took to the courts to challenge the government's action. On Dec. 15, 1976, the British Court of Appeal ruled that the government had exceeded its authority in ordering the CAA to revoke Laker's license, and it was effectively revalidated.

In February, 1977, Britain conveyed to the United States that it wished the U.S. government would resume processing to the Laker application for a foreign air carrier permit, clearing the way for the CAB's approval, President Carter's approval, and subsequently the start-up of the Skytrain service.

Meanwhile, the dual designation provision of the U.S.-British air agreement is a problem on this side of the Atlantic too - although it is only of the problems that CAB chairman Alfred E. Kahn may have had in mind at a recent congressional hearing when he referred to the pact as "that damned agreement."

Although Pan American World Airways and Trans World Airlines both had authority from the United States to fly to London from a number of the same cities, there were only two American cities served by both to London when the agreement was signed in June: New York and Boston. So there was no immediate problem when dual designations were required by Nov. 1 by President Carter, he named Boston and New York as the two cities that would get service by two U.S. carriers to London.

A serious problem is fast approaching, however. Pan Am had pulled out of Los Angeles several years ago under the terms of a route swap agreement between it and TWA - AN agreement that ends in March, 1978. Pan Am has said it plans to begin serving Los Angeles again when the agreement ends. It aslo wants to keep New York and Boston. So does TWA.

Aware of the potential problem, Carter had approved Boston and New York as the two cities for dual U.S. flag designation "on an interim basis" until further evidence could be heard on whether or nor Los Angeles should replace Boston in time for next year's summer travel season.

The board has said it will receive comments on the dual designation question within the 14 days following Carter's formal signing of an order implementing his recently announced decision on the expansion of U.S. air service across the Atlantic.