Thousands of cancellations by would-be air travelers and a 40 per cent reduction in scheduled flights kept British Skies unexpectedly orderly today on the first day of a strike by assistant air traffic controllers.

Most of the canceled flights belonged to British Airways, the nationally owned carrier. But senior air traffic controllers managed to get other flights in and out of London's airports with minimum delays.

Both airline and union officials warned that the situation could deteriorate as the four-day strike, the first ever by assistant controllers, continued.

Adding to the fears of further problems were work slowdowns by air controllers in Spain and France, as Europe's busiest holiday weekend turned into a testing time for those seeking the sun.

In Paris, French air traffic controllers today began a 10-day slowdown over pay and working conditions, causing many delays, but no flight concellaions. At Paris' two main airports, Roissy-Charles de Gaulle and Orly, nearly all incoming and outgoing flights had initial delays of 15 to 90 minutes.

Americans on both sides of the Airport said the situation was in hand primarily due to many passengers cashing in their airline tickets to crowd boat ferries to Europe.

Ferries were completely packed while some airlines admitted that flights had left for Europe with empty seats.

Officials have estimated that one million passengers have made plans to fly in our out of Britian this weekend, a four-day holiday in England and traditionally a time when many American and other tourists return home.

The controllers still on duty by-passed the function of their assistants by having airline pilots or crew members work out and transmit their own flight schedules. The assistants usually do this on computers.

A spokesman for the striking union charged the Civil Aviation Authority (CAA) with allowing massive breaches of safety in its efforts to keep planes flying. But the CAA said it was simply returning to a system used before computers were installed 2 1/2 years ago.

The British Airport Authority (BAA), which owns and manages seven major British airports hit by the strike, said airlines were reporting cancellations by 40 to 50 per cent of booked passengers today.

"This is largely responsible for the quietness at the airports now," said a spokesman. "They've made alternate arrangements."

British Airways cancelled 98 of its outgoing and incoming flights, 40 per cent of its total service. Most of these were either domestic flights or short-haul services to Europe.

U.S.airlines reported that two or three half-filled flights were combined, but otherwise all flights left as scheduled and incoming flights suffered delays of only a few hours.

"This is the most unusual Friday I've seen in weeks," said an employee of National Airlines, which runs a single daily flight between London and Miami. "Unsually it's full, now its empty. We've only got eight people in our first class. Usually it would be 30 to 35 . . ."