IN THEIR VEHEMENT struggle over the North Atlantic air routes, several British and American airlines now have drawn their two governments into an increasingly angry quarrel. Pan Am and TWA, both in dire financial trouble, urgently want to sell their London routes to United and American airlines. The sellers' survival may depend on completing the sales quickly. But they require the British government's approval and in return for it the British want, among other things, landing rights in more American cities for British Airways. The United States has (so far) refused that. Last week, to increase its share of a shrunken market, British Airways cut its transatlantic fares by a third. But that requires American approval, and the Department of Transportation promptly blocked it pending a resolution of the route sales. Two days later it approved a similar rate cut for Pan Am, blandly explaining that it was entirely different.

It's a bad time for the airline industry, whose distress accounts for the unusually sour temper of these negotiations. Worldwide, most of the industry forgot that it serves a highly cyclical market. In the booming 1980s, it bought great numbers of aircraft and loaded itself with debt. Now, with recessions underway both in this country and Britain as well as a war in the Persian Gulf, the airlines' overseas traffic is sharply down. The airlines can't shed their excess capacity, but at the same time, there isn't room for all of their flights at the world's principal airports.

The route sale is further complicated because, in the British view, the newcomers would be much more formidable competitors than the airlines they replace. In the American market, it's an enormous advantage for an airline to have an extensive system of domestic routes to feed its own transatlantic flights. Neither Pan Am nor TWA had them -- but both United and American do. To compensate for that new advantage, British Airways thinks that it ought to be allowed to fly to more American cities. The American rebuttal is that the situation's just the reverse in Britain -- there's only one airport, London's Heathrow, that international travelers want to use, and British Airways dominates it.

The sensible solution is another dose of deregulation to take governments out of these political disputes about who flies where. Crowded airports need to decide how much traffic to accept on each route and then put the landing rights up for auction. In this quarrel the British and American governments are vigorously representing the interests of certain airline companies. But they aren't doing anything for the interests of the airline industry as a whole, much less those of its customers.