The most important new car developed in Britian in two decades goes on sale here this week. Its success could determine the survival of Britian's auto industry and the future of much of Prime Minister Margaret Thatcher's strategy for restructuring the country's ailing economy.

The car is British Leyland's subcompact Metro, a completely restyled, hatchback version of the revolutionary Mini, which since its introduction 21 years ago has remained the British auto industry's biggest selling single model. The Metro, like the Mini, is primarily designed for the European Market.

Almost as small as the Mini on the outside, the Metro is more spacious, comfortable and flexible inside. It boasts fuel economy of up to 58 miles per gallon at a steady 56 miles per hour, and is being sold as cheaper to service than its small car competitors from other countries.

The Metro will not be sold in the United States, however, because adaptation to regulations there would greatly increase its price, which starts here at the equivalent of $7,500.

The Metro is the first car to be entirely designed and built under new management that is trying to transform government-owned British Leyland, the world's seventh largest automaker, from an unwieldy, strike-born, loss-making giant turning out notoriously undependable cars into a model for the kinds of changes Thatcher wants made throughout British industry.

Under Sir Michael Edwardes, a feisty South African who has been company chairman for the past three years, the loose collection of nationalized factories that make everything from Minis to Triumphs, Jaguars and trucks have been ruthlessly reorganized and streamlined.

Edwardes has shut 13 factories and shed 30,000 of 150,000 employes, with more cost-cutting still to come. He has stopped production of some uneconomic if widely admired models, including the MG sports car, and promoted the expensive, government-financed development of replacements for other models considered antiquated.

With brinkmanship tactics, Edwardes has convinced workers, sometimes over the objections of their union leaders, to accept lower pay raises and flexible new work rules while avoiding the wildcat strikes that had made the autoworkers the scourge of British industry. One company-wide strike ended within days after Edwardes warned that the alternative would be British Leyland's immediate collapse.

After more than 500 wildcat strikes in the last three years, the company has gone without such disputes for more than 98 percent of its working hours during the past six months. Edwardes calls this a "total revolution" in industrial relations.

For production of the Metro, two new assembly lines were built at the 17-acre, 70-year-old plant at Longbridge in Birmingham. The Metro assembly lines, the most modern and automated in Europe, are run by computers and use giant robot arms for much of the most difficult and exacting body work, including all the welding.

Although this elminated more jobs and required unprecedented cross-jurisdictional work for many unions, the workers have gone along. They have been convinced by Edwardes that the Metro is vital to the future of remaining jobs. And they have been impressed by the unusual sight of top managers spending seven days a week on the factory floor.

To eliminate the reputation for unreliability that helped cut its share of the British car market from 40 to under 20 percent in recent years, British Leyland applied expensive Japanese-style intensive testing to every Metro coming off the asembly line. Edwardes also has threatened British suppliers that he will switch to their foreign competitors unless they provide more reliable parts at better prices.

These suppliers are among a multitude of British businesses with hundreds of thousands of employes, including the government-owned steel industry, whose future depends on the survival of British Leyland -- and thus on Metro's success.

Metro is crucial, Edwardes says, to building a new British Leyland reputation for innovation, reliability and economy among car buyers here and in the rest of Europe.

Company executives hope Metro will greatly increase public expectations for other new, more profitable models coming in the next few years, including a Japanese-designed sports car being built jointly here with Honda and a line of larger family and fleet cars. British Leyland will continue making its still successful Rovers, Jaguars and trucks, as well as the original Mini, which has sold 5 million cars and imprinted its name on the English language.

But British Leyland's future remains clouded. After consuming more than $2 billion in government money since 1975, the company will still need more to finance model development before it hopes to start turning a profit in three or four years. It also will require continuing innovation and cost-cutting cooperation from its management and work force, which for a second year has been offered pay raises averaging only about 6 percent -- well below the current 16 percent inflation rate.

Critics accuse Edwardes of being heavy-handed and unrealistically optimistic about the chances of his strategy saving the company. "All I can say is that we've stayed in business several years longer than everyone said on the day when I took this job," Edwardes said recently. "Our major success is that so far we've survived."