Britian's cities were relatively calm last night and early this morning, but hit-and-run gangs of youths once again broke windows, looted stores and clashed with police in scattered, mostly minor disturbances during the country's 10th consecutive night of urban unrest.

The most serious trouble occurred in Leicester in the industrial Midlands, where about 500 black and white youths in a large public housing project overturned and burned cars and attacked police and firemen with bottles and molotov cocktails.

In London, where rioting had been the most widespread early in the weekend, the only disturbance last night was caused by youths who broke store windows, looted some shops and threw bottles and bricks at police in the racially mixed Notting Hill neighborhood near the fashionable West End.

But London generally was so quiet that Prime Minister Margaret Thatcher, who had spent Saturday night at Scotland Yard, discussing how police coped with the disturbances, went to the theater to laugh during a benefit performance of a comedy satirizing her.

Police officials in a number of cities described the trouble now as primarily "hooliganism" and "vandalism" by the hit-and-run gangs of teenagers in contrast to the earlier fierce attacks on police and property by much larger, frenzied mobs.

Authorities estimated that 1,200 people were arrested in rioting in 20 cities across the country during the weekend.

Thatcher spent eight hours watching the police officials in London supervise an intense operation that resulted in 160 arrests, most of them in the Brixton and Battersea areas south of the Thames River. The police operation noticeably reduced the rioting in the area.

Thatcher made no public statement. But officials said she met with top authorities at Scotland Yard and visited with officers at Brixton who had been battling rioters for days. She also reportedly talked with the mother of a teen-ager arrested in Brixton -- where many families of West Indian origin live in a crowded neighborhood with an unemployement rate of more than 50 percent for young adults.

William Whitelaw, the home secretary, publicly emphasized the government's determination to restore order and improve protection for the police as its first priority.

"We have had too many injured," Whitelaw said of the police, whose conduct in quelling the riots he unreservedly praised. "It is the duty of the government to make sure they are protected."

He also reiterated his belief that political extremists had moved onto several trouble spots after the rioting began.

"There is no evidence of any overall control or design, and criminal hooliganism cannot be designed," Whitelaw said. "But agitators have moved around, there is no doubt about that."

The geographical spread of the rioting during the weekend is striking. It hit the racially mixed, high-unemployment inner-city neighborhoods in London, Birmingham, Manchester, Leeds, Nottingham, Leicester and other industrial cities and towns hard hit by Britians's worst racially mixed gangs of youths also caused serious damage in towns like Luton and High Wycombe in the rolling hills of the urban counties around London, the port of Southhampton and the working-class, seaside resort of Blackpool in Northwestern England.

The deputy leader of the opposition Labor Party, Denis Healey, yesterday made his party's strongest statement alleging that Thatcher's monetarist economic policies were an underlying cause of the trouble in British cities.

"Britons will never feel safe again in their homes and streets until the policies that have produced unemployement and decay have been reversed," Healey said in a speech. He accused Thatcher of blaming everyone but herself for the rioting.

The government must take action to offer our youngsters hope," Healey said, "and take it before next week's unemployement figures send another wave of despair across our land."

[Meanwhile, in Northern Ireland, a man was stabbed to death and rioting youths showered British troops with acid and gasoline bombs after eight nationalist hunger strikers rejected a mediation effort to end their hunger strike, United Press International reported. Police gave no details on how the man died.]