British Airways said yesterday it will ask the United States and British governments for permission to extend cut-rate transatlantic air fares to most of the American cities it now serves, including Washington.

BA's action suggests strongly that the British Government must have acceded to U.S. demands to allow low-fare proposals to go into effect during the negotiations now taking place in Washington. U.S. air officials were in the negotiations yesterday and couldn't be reached for comment.

Citing the successes of cut-rate air fare between New York and London that were in effect since September, both Pan American World Airways and Trans World Airlines said in January that they wanted to extend the low fares to other cities as well.

While the Civil Aeronautics Board here had no objection, and indeed has encouraged low international fares along with President Carter, the British Government expressed its "dissatisfaction" with the proposals.The British also turned down low fares proposed by Braniff Airways on its new route between Dallas and London, delaying the March 1 inaugural of Braniff's new service indefinitely.

The British have so far taken the view that the low fares from New York were experimental and ought not to be extended to other cities until after at least one-year period.

Both the Braniff situation and the British rejection of other U.S. carriers' low-fare proposals have dominated the U.S.-U.K. talks, which started a week ago Monday and are scheduled to continue through Friday, although a charter services agreement between the two countries was the originally scheduled topic.

The talks started on the day President Carter announced he agreed with the CAB that British refusal to approve Braniff's proposal fares violated the US-UK air agreement and that he would consider tretaliating against British Caledonian Airways if the negotiations failed to produce a "satisfactory resolution." No announcements about the talks have as yet been made by either side.

British Airways said yesterday it wanted to extend low-cost standby fares to seven cities besides New York starting Saturday. If approved, travelers would be able to fly standby to London for $162 from Washington, $143 from Boston, $151 from Philadelphia, $169 from Detroit, $171 From Chicago, and $227 From Los Angeles or San Francisco. Fares back to the U.S. would be slightly lower, as are fares to New York. A BA spokesman said the fares would probably go up about $25 each way during the summer months.

Both Pan Am and TWA had proposed similar, if not the same, fares and can now be expected to institute them as well.

BA said a maximum of 350 seats will be made available each week per city in each direction are made available in New York.

Besides the "standby" plan, the same fare is available to passengers requesting seats at least three weeks in advance who are willing to go on a day the airline selects in the week of the passenger's choice.