Transatlantic airlines, already hit by declining passenger traffic in the midst of their normal peak travel season, yesterday began a new round of fare-slashing aimed at luring customers during the off-peak season.

So far, the fare cuts affect only routes between the United States and London.Fares to other European destinations are likely to be affected as the airlines approach their slow period, especially if potential travelers are diverted to London from other possible points by the low fares.

Although some proposed fares changed almost hourly yesterday as airlines sought to undercut each other -- mostly in the New York market -- it appeared toward the end of the day that Washington-area travelers have a good chance of traveling nonstop to London after Sept. 15 for less than $400 round trip.

The reduced fares, effected Sept. 15, are subject to almost certain approval by the British and U.S. governments.

British Airways, which flies daily Boeing 747 service, will offer a one-way standby fare to London for $198. The fare is good through May 14, 1981. The $396 round-trip fare compares with an off-peak standard economy fare of $984 round trip. Passengers using standby tickets will have a reasonable idea about their chances on a given flight but can't be certain.

For passengers who wish confirmed seats, BA also will offer a lower advance-purchase "Dollarstretcher" round-trip fare of 494. Tickets at this fare must be purchased 21 days in advance; users can stay one week or up to six months. There is a $50 cancellation fee if the trip is cancelled within the 21 days.

Trans World Airlines matched BA's advance-purchase fare on its connecting service through New York.

Pan American World Airways, which also flies nonstop to London from Washington, did not partake of yesterday's fare action but is likely to match BA's fares.

Yesterday's rash of fare-cutting also involved London routes to New York, Boston, Chicago, Philadelphia and Los Angeles. By the end of the day, Twa and BA New York standby fares for the fall were lower than Laker Airways' cheapest ticket.

"We are not going to be in the market place with higher fares than anyone else." TWA Vice President Neil M. Effman told a London news conference.

Airline officials are hoping the lower fares will turn around the sagging transatlantic business. The current economic environment has taken its toll on travel, with Americans additionally deterred from visiting Europe because of the high cost of land accommodations and the poor exchange rate.

Offsetting somewhat the decline in the numbers of Americans traveling is an increase in the number of Europeans visiting the United States, which appears to be the bargain spot to many.

In another development, World Airways said it would begin offering a new standby fare on its scheduled service to London, effective immediately if it gets British government approval.

World said it would offer a one-way standby fare of $208 for its economy class or $399 for its first class seats on flights originating from Baltimore, Boston and Newark.