Citing the successes of three-month-old cut-rate fares between New York and London, both TWA and Pan Am said yesterday they want to extend the low fares to London from other cities, including Washington.

Both carriers are among the six airlines on the dense New York-London route which responded to the introduction of Laker Airway's low-cost, no-reservations Skytrain passenger service in September with a package of three low fares of their own. Until now, two of the fare offerings - within $20 of Laker's $238 round-trip fare - have been limited to the New York-London market.

Yesterday, Trans World Airlines asked thr Civil Aeronautics Board for permissin to introduce "stand-by" fares - with reductions of more than half the current coach fares - from Boston to Philadelphia, beginning April 1.

Also yesterday, Pan American World Airways said it would ask the CAB on Monday for permission to institute a "budget" fare of $283 round-trip between Washington and London, beginning Feb. 23. The new fare - $162 to London and $121 back - would be less than half the current round-trip regular economic fare of $680 between the two cities.

Pan Am said it would also propose budget fares from Boston to Detroit.

Under Pan Am's proposal, a maximum of 350 seats in each direction would be made available each week at the proposed fares. To take advantage of the fare, a traveler picks the week in which he or she wants to fly and buy a ticket at least 21 days in advance. At least seven days prior to that week, the passenger is informed of the exact date and time of departure.

For the return flight, the passenger is notified of the exact day and time of return seven days prior to the week of return requested before departure from the U.S. or during the stay abroad.

In contrast, TWA proposed cut-rate fares using a stand-by arrangement - with no advance booking or guarantee of getting a seat. Seats would be assigned after 4 a.m. on the day of the flight and could not be bought within three hours of the flight time in the U.S., or within two hours in London. There would be a limit of 350 seats in each direction each week.

Between Philadelphia and London, TWA's proposed stand-by round-trip fare of $265 ($151 eastbound and $114 westbound) would be $375 less than the current regular economy fare of $640, TWA said. The proposed rould-trip fare between Boston and London would be $250 ($143 to London and $107 coming back), $366 below the economy fare of $616.

"The popularity of our no-reservations fare in the New York-London market has encourage many Boston and Philadelphia passengers to travel to London via New York rather than use more direct TWA services," Donald M. Casey, TWA's senior vice president for marketing, said yesterday in explaining why TWA decided to expand the fare to other cities.

The standby and budget fares offered by TWA, Pan Am and other member carriers of the International Air Transport Assosciation between New York and London are $146 eastbound and $110 westbound, compared with Laker's $135 eastbound and $103 westbound fares.

Given the CAB's predisposition toward low fares and President Carter's tenacious pursuit of fare competition in international aviation, it is unlikely that the U.S. would disapprove the airlines' proposals.

It is unclear what the British Government will do, but it did approve the similar London-New York fares now in effect. Presumably, British Airways would seek to meet the new fares.