Serious rioting broke out for the third time in less than a month in Britain tonight, as youths battled police in the Tottenham section of north London in clashes that left one policeman dead of knife wounds and at least 60 persons injured.

Two other policemen were wounded by shotgun fire, and one was reported in serious condition. It was the first reported use of firearms by rioters in the series of disturbances in economically depressed, primarily black areas in recent weeks. At least two journalists also were wounded with shotgun pellets.

A police spokesman late tonight declined to specify the number of arrests, but he said that the situation appeared to have reached a tense standoff, with police reluctant to advance until morning into tenement houses to which rioters had retreated.

"We are in a position of containment now rather than making arrests," the spokesman said.

Street battles lasted for several hours, as hundreds of youths pelted police with firebombs and bricks. There was no indication of who had fired what reportedly were several shotgun volleys at police. Numerous overturned cars, some of them formed into barricades by the rioters, still flamed in the streets, which police had closed to traffic.

Most of the injured were policemen, who repeatedly charged the rioters, wielding truncheons from behind body-length Plexiglass shields. Some of the shields also caught fire after being hit by gasoline-filled bottles stuffed with flaming rags.

Although there were no reports of police use of firearms, special squads of officers equipped with rifles loaded with plastic bullets reportedly were deployed in the area.

Tonight's rioting was sparked by the death yesterday of a West Indian woman, Cynthia Jarrett, who collapsed when police raided her home. Police said they attempted to resuscitate her but that she died on the way to the hospital. They said they had entered the house in search of stolen property after the arrest of Jarrett's son, Floyd, for suspected auto theft.

As word of her death spread yesterday, a small group of protesters gathered outside the Tottenham police station but eventually left peacefully. A larger number gathered today, however, and by nightfall groups of youths, both black and white, had assembled on the streets. The rioting began soon afterward, when they attacked riot-equipped police who attempted to disperse them.

Tonight's rioting was the third in a series of major disturbances that began last month when black youths took to the streets in the low-income Handsworth district of Birmingham, Britain's second largest city. The government has said that "criminal elements" were in large part responsible for stirring up the trouble. Many local residents, however, attributed the violence to increasing unemployment, particularly high among young blacks, and what they say is racially-based harassment by the overwhelmingly white police force.

Large disturbances broke out eight days ago in Brixton, a poor south London neighborhood, that time more directly related to an incident involving the police.

On Sept. 28, police accidentally shot and wounded Cherry Groce when they forcibly entered her home in search of her son, Michael, in connection with an armed robbery. Mrs. Groce is still hospitalized and is paralyzed from the waist down.

The shooting of Mrs. Groce and an incident in August in which a five-year-old boy in Birmingham was accidentally shot to death in his home by police looking for his father, gave rise to a new round of questions concerning police use of firearms in Britain. Long considered an unnecessary hazard and provocation in police work, guns until recent years were issued only to elite units of officers for special assignments. As the criminal use of weapons has increased along with a rising crime rate here, however, police officials have argued that their own increased use of firearms has been justified.

The riots during the past month have been the worst since 1981, when numerous inner-city neighborhoods erupted in what youths said were protests against police methods in black communities.

As a result of the 1981 riots, the government appointed an independent committee that recommended increased public spending on depressed urban areas and extensive changes in police procedures.

Despite the establishment of numerous police-community liaison groups, however, local residents in Brixton say that the situation is little improved. Community leaders say that ongoing difficulties with police, combined with rising unemployment, has made the inner-city neighborhoods increasingly volatile.