U.S. and British negotiators have tentatively agreed to liberalize terms of the controversial Bermuda II aviation agreement to expand air services between the nations , sources said yesterday.

During consultations just concluded in London, there was apparent consensus to:

Allow each nation to name five U.S. cities to receive new nonstop service from London over the next three years.

Let the United States add an additional American carrier to a U.S.-London route that is currently served by just one U.S. airline.

Although the Bermuda agreement currently allows air services between Britain and 16 U.S. cities, only one U.S. flag carrier can serve each route except for New York-London and Los Angeles-London, which both have "dual" designation. Although the negotiators didn't pick the city, it is widely expected that Boston would be picked up by the U.S. to be served by two U.S. airlines since it lost dual service when Bermuda II was signed in mid-1977.

Since the agreement was signed, U.S. officials have complained that its provisions are too restrictive and do not comply with the pro-competition international aviation policy enunciated by the administration shortly afterwards.

U.S. officials recently have expressed optimism that the British might be willing to expand the agreement since its two major airlines both wanted to begin new routes to the United States.

No formal agreement was reached in London, but additional meetings were set up beginning Feb. 27 here to resolve unsettled issues and formalize the new provisions. No progress was reported in London on U.S. initiatives to give airlines more freedom to set their own prices without governmental interference.

Another unsettled issue is whether airlines on the new routes will be awarded a period of monopoly service to get their services going. The British are said to want their carriers to have a three-year headstart over any American carriers on the cities they pick.