INTO THE BREACH U.S. tourists return to Europe

''The downward spiral has stopped.'' So said Sally McElwreath, a Trans World Airlines official, as she described faint but encouraging signs last week that the dramatic drop in U.S. tourist travel to Europe had at last bottomed out. Most airlines were reticent about releasing figures, but British Airways reported that bookings, down to a mere 5,000 a week after the U.S. air attack on Libya in April, had risen to more than 60,000, just 3,000 short of the figure for the same week last year. Pan Am's reservations have been increasing 8% to 10% a week for the past three weeks, and TWA reported that telephone inquiries about flights to European destinations had jumped 80% since last month. Says Merle Richman, a Pan Am spokesman: ''There is a feeling that we are breaching a psychological barrier.'' If so, winning the breach has cost plenty. In order to woo back nervous travelers concerned about Arab terrorism, Soviet radioactive fallout and the declining U.S. dollar, airlines were engaging in extraordinary gimmicks and severely cutting their prices and profit margins. In the forefront of the European scramble to recover American business is British Airways. BA has waged a $6 million promotion campaign called ''Go for it, America'' to win back U.S. travelers. That effort reached a climax of sorts last week when 5,791 American winners of a BA sweepstakes were given free flights to London. Even Prime Minister Margaret Thatcher got into the act when she invited 30 of the sweepstakes winners to join her at 10 Downing Street for tea. For its part, Pan Am is offering free car rentals and two-for-one ticket deals to help fill seats on its Europe-bound planes. The airline is heavily promoting its new ''Alert'' security measures, which place armed guards and sniffer dogs in most Pan Am terminals. TWA is offering similar incentives, but last week the troubled airline, which has just weathered a ten-week strike by flight attendants, suffered another jolt with the departure of President Richard D. Pearson. Heartening as the rise in bookings was for airlines and travel agents, it was noteworthy that most of the increase came from individual American tourists, rather than from the group tours that traditionally make up 25% of the transatlantic summer-season business. ''The group travelers are a little greener, a little more skittish,'' says Pan Am's Richman. For all the indications that the tourist slide had stopped, however, the doleful fact remained that the European tourist business this summer will remain rotten, especially compared with 1985, when a record 6.4 million Americans crossed the ocean. Says Carlo Mole, chairman of C.I.T., Italy's largest tour operator: ''It is useless to kid ourselves. This season is done for.''