Civil Aeronautics Board Chairman Marvin S. Cohen yesterday warned United States airlines flying to London that they could lose their routes there if they fail to offer the public low air fares.

In a speech to the International Aviation Club here. Cohen noted that passenger traffic across the North Atlantic last summer was up more than 40 percent over the summer of 1977 and consumers had paid an average of 15 percent less -- about $50 million -- for their tickets.

Lively competition, especially from the new carriers -- Braniff International, Delta Airlines, National Airlines, Laker Airways and British Caledonian Airways -- made the difference, he suggested.

But Cohen complained that on most routes to Britain, restricted by agreement to one U.S. airline, passengers were not offered lower cost fares on Pan American world Airwaysand Trans World Airlines, the airlines that have traditionally held the British routes, to the same extent they are being offered by the new entrants.

Ten of the U.S. cities which get nonstop service to London are controlled by incumbents "who appear to be less-than-enthusiastic advocates of low fares" and are "quite content with the status quo," Cohen said.

"The thought of bludgeoning airlines into being innovative and competitive is not esthetically very appealing to me, but neigther is monopoly pricing," Cohen said. "I plan to counsel the board to consider fully the possible transfer of operating authority when monopoly incumbents prove unwilling or incapable of being aggressive competitors."

When an international agreement limits the United States' right to name multiple airlines to serve a route -- as with the British agreement -- those designations become "a scarce resource," Cohen suggested. Under the Federal Aviation Act and the President's international aviation policy, he said the board had an obligation to assure on a continuing basis that these resources are allocated in an economically efficient way.

Cohen's speech, his first on international aviation policy since becoming chairman of the CAB three months ago, focused on transatlantic travel primarily but he siad the same policy considerations apply to transpacific travel. He noted, for example, that the average fare to Japan is now one of the highest per-mile fares in the world although direct operating costs are among the lowest.