President Carter yesterdy approved the proposal by Laker Airways of Britain to initiate no-frills, no-reservations Skytrain air service between New York and London at a one-way fare of $135.

The President acted exactly a week after the Civil Aeronautics Board recommended that he permit the cut-rate flights across the Atlantic for a one-year trial period.

The speedy action by the President - some international air decisions have sat in the White House for months - is attributed in part to the fact that his approval of the Laker application may aid United States negotiators during the current talks with the British government to work out a new agreement on scheduled air services between the two countries. The existing agreement expires on June 22.

In addition, the President already had enunciated a foreign air policy favoring price competition.

Robert M. Beckman, Laker's Washington attorney, yesterday said it is possible that the Laker Skytrain could begin flights in the latter part of August. Under the board's recommendation, which the President signed without any modifications, the Laker service could begin 60 days after Laker files a formal tariff with the board. Beckman said he expected to file the tariff early next week.

The 60-day lead time was designed to allow the U.S. carries with New York-London routes - Pan American World Airways and Trans World Airlines - time to develop, if they wanted to, competing but not necessarily identical, services to match Laker's fares. Both airlines have said they will.

The two-month period also will give the two governments time to work out any kinks in the proposal.