President Carter has asked Britain to allow two U.S. airlines to offer non-stop service between London and three American cities, instead of two as provided in last year's U.S.-U.K. aviation agreement.

British acceptance of the proposal would relieve the president of the politically difficult decision of having to choose between Los Angeles and Boston as the second city.

Currently, both Pan American World Airways and Trans World Airlines provide nonstop service between London and New York and Boston on the other.

But the Civil Aeronautics Board tentatively has decided to recommend to the president that the two American cities to be served by two carriers to London should be New York and Los Angeles, and that TWA should be the single carrier from Boston.

Eliminating Pan Am from Boston would mean a loss of jobs, and important Massachusetts politicans - including House Speaker Thomas O'Neill Jr. and Sen. Edward Kennedy - were not reluctant to point out to the president.

In a "Dear Jim" letter sent to Prime Minister James Callaghan Tuesday, Carter said the United States would formally designate Boston, Los Angeles and New York City to be linked by nonstop service with London tby two U.S. airlines, even though he realized that under the Bermuda II agreement, Britain is obliged to accept only two U.S. cities for such service.

"I hope you will not take this step and thereby limit our designations to two cities," he wrote Callaghan. "We would in return be prepared to make comparable new competitive opportunities available to your airlines.

"I hope you will agree that additional air service, and the healthy competition it will bring, will be of benefit to our citizens and will ensure the continued growth of commerce between our nations," he concluded.

It is not clear what the British reaction will be, or what they might consider a fair trade for the additional city for the Unted States.

One source suggested that Freddie Laker, the ebullient head of Laker Airways which now flies between New York and London, might be able to convince the British to approve the U.S. proposal Laker is allowed to fly to London from Boston as well.