Reacting to riots in British cities and facing a censure motion in Parliament, Prime Minister Margaret Thatcher today announced a billion-dollar government program to slow the rapid rise of unemployment in Britain, especially among young people.

The program's announcement marked a significant departure from Thatcher's resistance to using government money to ease the country's recession, and was seen here as a victory for cirtics in the prime minister's Cabinet who have called for such measures to combat the 11.8 percent unemployment rate, which is threatening to rise above the records of the Depression of the 1930s.

Thatcher appears to have been forced to agree to the new plan by her Conservative Party's concern over the potential political damage resulting from the joblessness and recent rioting among young people in many British cities. Today's announcement contrasted with Thatcher's previously heavy emphasis on law and order as the remedy to the violence.

There were new disturbances over the weekend in the Lake District resort town of Keswick and in Liverpool's riot-torn districts, although authorities said they were not as extensive as those of recent weeks.

Thatcher's government was easily able to defeat a censure motion tonight introduced by opposition Labor Party leader Michael Foot, who called the new program "a derisory package." But Conservatives fear they could lose the next national election in 1983 or 1984, despite the advantage of facing an ideologically fragmented opposition.

In announcing the new program Thatcher said more places would be provided in government training and temporary make-work programs for teen-agers leaving school who cannot get jobs. The government also will pay private employers a cash subsidy of nearly $30 a week for each dropout they hire at a salary of less than $80 a week. Only one of every two teen-agers leaving school has been able to work in recent months.

More government money also will be spent creating extra places in secondary schools and colleges for students who want to continue their studies, Thatcher said, and technology centers will be set up in inner cities to train jobless young adults in computer and electronic assembly skills.

Thatcher told Parliament the new measures would cost $285 million this year and $760 million $950 million next year.

Unemployment in Britain is rising steadily and has reached 2.8 million, including 900,000 teen-agers. Officials have addmitted privately they hope today's measures will prevent joblessness from reaching the 3 million mark.

"We must continue to provide for those who leave school but who fail to find work," Thatcher said, adding that the government already is spending about $2 billion keeping 800,000 teen-agers off the unemployment rolls. The new steps and injections of extra money into old programs may provide alternatives to joblessness for another 400,000, according to initial estimates today.

Thatcher said the job-subsidy scheme, added by her monetarist economic advisors to proposals made by her chief Cabinet critic, Employment Secretary James Prior, is designed to restore for younger workers jobs that were destroyed in recent years by "unrealistic pay bargaining." This is why, she said, the government was helping those employers who could hire teen-agers for lower-paying positions.

The most recent surveys of business leaders and forecasts by economic analysts still indicate no end in the near future in Britain's deep recession. But Thatcher insisted in today's parliamentary debate that "there are signs of success. There are signs that our policies are working in advance of an upturn in the economy."

She cited a slowing of wage and price inflation and an increase in efficiency of british business, largely through the shedding of jobs. But Sir Terrence Beckett, director of the Confederation of British Industry, recently told a group of American journalists here that "the problem is you need a big upturn to take advantage of these improvements."

There is no sign at all in our forward look, no indication at all of an upturn," Beckett said of his group's surveys of British businesses."There is no reinvestment in sight. The money is there, but not the profitable opportunities to invest it. And British industry is very concerned about unemployment and inner-city decline."