Britain's first national steel strike in more than a half century began today, threatening further harm to the nation's troubled economy and confronting Prime Minister Margaret Thatcher with her first domestic crisis.

More than 100,000 steelworkers walked off their jobs this morning in a dispute over pay and the loss of tens of thousands of jobs at the already ailing, government-owned British Steel Corporation. Tonight, other union leaders promised not to cross their picket lines or to transport imported or privately made steel, effectively blocking all steel production here during a strike that both unions and management fear could last several months.

Although Britain's biggest, manufacturing industries had stockpiled up to a month's supply of steel in anticipation of the strike, they now may not be able to move it into their plants. A long strike threatens the survival of not only British steel but also many of these similarly declining heavy industries -- particularly car and home appliance manufacturers.

The steel strike was pronounced "100 percent" effective tonight by Len Murray, general secretary of the Trade Unions Congress, the British AFL-CIO. "What we have here," said Murray, who tried desperately to avert the strike through his own mediation, "is a dispute which has not been sought either by British Steel or by the unions, but which stems from the excessively rigid attitude of the government and its determination to impose its theoretical monetary policies."

At the heart of the strike is Thatcher's survival-of-the-fittestt prescription for curing the British economy under which large pay raises are to go only to workers who earn them with increased productivity and jobs are to be preserved only when they can be paid for with profits, even in nationalized industries.

"You can't just take out more in pay without more productivity," Thatcher said yesterday in discussing the impending steel strike. "And the only security for jobs is to make an industry more efficeint and profitable."

British steel has been losing more than $2 million a day and has consumed nearly $10 million in government subsides over the past six years against a contracting world market and cheaper foreign competition. It originally offered its 150,000 total employes only a 2 percent pay raise, while the unions demanded enough to cover Britain's inflation rate, now soaring above 17 percent.

Under threat of the strike, the wage offer was increased to 6 percent provided the unions cooperate with work rule changes to increase productivity and help cut 12,000 of the 52,000 jobs British steel executives believe must be eliminated to stay in business.

This was too much to take for Britain's steel union, the iron and Steel Trades Confederation and its president, William Sirs, who have been considered a moderate trade union leader here. They had already cooperated with British Steel, which was nationalized in 1967 in the elimination of 30,000 ain's steel union, the Iron and Steel jobs in the last four years, mostly with generous severance payments.

"While I have been cooperative and kept things low key, there has to be a time when you cannot go any further along the same route," Sirs said when the 2 percent pay raise was offered. Job cuts were one thing, he said, but the combination of job cuts and low pay unified his members to risk a strike, the first to shut down the British steel industry since 1926, that could cost them even more jobs.

The success of the strike for the unions depends on their stopping imports of finished steel from firms in other European countries and Japan or to be processed by Britain's remaining profitable private steel companies which produce a quarter of the country's steel.

Since nationalization, the British Steel Corp. has spent huge sums reorganizing into giant, modern Japanese-style plants with massive capacities. rIt could produce 34 million tons of steel this year, but expects orders for only about 15 million tons. The energency program of cutbacks is to shut down some very recently modernized plants.

While Thatcher does not believe in setting national pay norms, she is trying to squeeze the money supply and keep down subsides to nationalized industries, both to reduce inflation and to make money unavailable for giving pay raises or saving jobs that are not justified by increased productivity and profits.

This policy has been attacked publicly by the opposition Labor party and the unions and is worrying some business leaders and members of her own cabinet. They fear it will only deepen Britain's coming recession, bankrupt both private and government-owned firms, and drive unemployment from the present 1.3 million jobless Britons, already half the number out of work in the depths of the Great Depression, to nearly 2 million by the end of this year.

Until this strike, Thatcher had believed her plan was working. Although pay raises so far this winter had hovered near the inflation rate of 17 percent, some of the larger increases had been in firms with good profits or agreements to increase productivity while unions agreed to raises of as little as 5 percent in some struggling firms.

There also had been no crippling strikes, like those of government employes and truckers last winter that pushed the old labor government out of power or the mineworkers strike in 1974 that brought down the last Conservative government.

This winter, the miners stayed on the job after getting a 20 percent pay raise, including productivity bonuses, a month ago. That pleased Thatcher but made 2 or even 6 percent much more unpalatable to Sirs' steelworkers.