The turmoil in British labor relations continued to tilt in favor of government and industry yesterday as striking auto workers at Austin Rover rejected the advice of their shop stewards and voted overwhelmingly to return to work. Meanwhile, the drift back to work of striking coal miners continued.

Although the long and violent miners' strike has captured the headlines and the nation's attention for more than eight months, Britain recently has been hit by a variety of other walkouts, particularly in the auto industry.

Today's back-to-work vote by about 11,000 Austin Rover workers at the firm's big Longbridge plant near Birmingham signaled the total collapse of the strike that was begun Nov. 5 by about 28,000 workers at several factories. The strike had started to crumble soon after it was launched, with the unions divided over the pay provisions. The Longbridge plant was the last in which workers defied union advice and went back.

The strike is being viewed by British commentators as a victory for both the government's tough, new trade union laws and the company's stance in refusing to budge from its offer of a 10.2 percent wage increase over two years. The union wanted it in one year.

The new trade union act, passed just two months ago, makes it compulsory for unions to hold secret ballots of their membership prior to strikes. Britain's umbrella labor organization, the Trades Union Congress, has opposed this.

But in the first major test of the legislation, Austin Rover management took the unions to court and won injunctions ordering the unions to comply. Two of the biggest unions -- the engineering workers and the general and municipal workers -- did so.

The company says production of 30,000 cars and about $175 million were lost during the walkout.

Another strike over wages at the Ford Motor Co. operations in Britain is now in its third day, with thousands of workers out after a walkout by about 270 sewing machinists halted the production line.

Last month, a strike at the General Motors subsidiary Vauxhall ended after a GM vice president warned that a drawn-out walkout could affect future investment plans here.

The state-run National Coal Board, which has been locked in a bitter struggle with the National Miners Union since March 12, declared today that another 824 miners had reported to work for the first time, bringing to 4,126 the number who reportedly have come back this week and to about 11,000 the number who have come back so far this month.

The drift back to work has been spurred by several factors, government officials say.

One is the Christmas package of wages and some bonuses that has been offered by the coal board in recent weeks. Another is the total collapse of negotiations, with the board saying it has made its last offer. A mine foremen's union accepted that offer but the main mine workers union will not. Another factor is the association of the controversial mine union chief, Arthur Scargill, with Libya and the Soviet Union in a search for assistance for the financially beleaguered miners.

The coal board figures, when added to the roughly 50,000 miners who have worked throughout the strike because the union declined to call a national ballot at the outset, mean that 61,000 of the union's 189,000 members are at work.

But there is no way to verify those figures independently. Scargill says they are bogus and that the coal board is using the press to cripple the strike. One problem is that there are only about 178,000 working miners, the rest being union members performing other duties. While union officials acknowledge that there has indeed been a drift back to work of pit workers, Scargill maintains that "over 140,000 miners remain on strike."

The best news for the coal board came in North Wales, which today became the first region to fully reverse the strike. The region has only two of Britain's 174 pits and about 1,000 miners, but it was still viewed as significant.

Whatever the correct back-to-work figures, top aides to Prime Minister Margaret Thatcher do not believe the end of the strike, which is now the longest and most violent in British history, is near and forecast it will go on into next year.

Last week, Norman Willis, the new general secretary of the Trades Union Congress, was hooted down while addressing a miners' rally and a hangman's noose was dangled in front of him when he warned miners that violence hurts their cause and denounced resort by pickets to Molotov cocktails and metal bolts as missiles.

But yesterday, Willis, who was praised by government officials for his courage, said it was "lunatic management" for the coal board to try to get miners back to work with Christmas bribes. "It is vitally important for the future of this country for the striking miners to go back to work with their heads held high," he said.