A senior British general was injured seriously today by an Irish nationalist bomb that tore his car apart as he drove away from his home in a quiet South London suburb.

Lt. Gen. Steuart Pringle, 53, commanding general of the Royal Marines, was reported in stable condition tonight after his right leg was amputated below the knee. The Provisional Irish Republican Army, which recently stepped up its campaign of violence aimed at ending British rule of Northern Ireland, claimed responsibility for the attack.

It was the second bombing by the Provisional IRA in London in a week. Last Saturday, two persons were killed and 39 injured, 21 of them members of the British Army's Irish Guards, when a bomb exploded outside the Army's Chelsea barracks in central London, about four miles north of the scene of today's bombing.

Police sources said they are searching for a Provisional IRA terrorist cell of four or five men who could be responsible for both attacks and may be planning more. They have circulated police sketches of the suspects based on descriptions of men seen near a laundry truck in which last Saturday's explosion was detonated as a bus filled with Irish Guards passed by.

Prime Minister Margaret Thatcher warned tonight that "it is absoutely vital that every member of the public should exercise extreme care and vigilance. Everyone should be careful, not just those who by virtue of their position may be attacked. Such vigilance will help to beat the danger and catch the perpetrators of these dreadful crimes."

The head of Scotland Yard's antiterrorist squad, Police Cmdr. Mike Richards, said "it is possible" that the bomb that exploded beneath Pringle's car today "was the same type of device" used to kill Airey Neave, a senior Conservative member of Parliament, when his car exploded on the ramp of the House of Commons underground garage here in March 1979. An IRA splinter group, the Irish Nationalist Liberation Army, claimed responsibility for Neave's death.

Pringle had just pulled away from the curb near his home in the suburb of West Dulwich at 11:30 a.m. when the bomb in his car exploded beneath his feet, blasting out the car's hood, roof and sides. The bomb that killed Neave exploded in the same way; it had been activated by a mercury device reacting to the car's movement after being started.

One of Pringle's neighbors, Mike Mullins, witnessed the explosion while waiting for a bus at a nearby stop.

"Suddenly, there was a big flash, and I saw the hood of the car fly up over a house," he said. "I rushed to the car, and I could see the driver, who was still conscious, but his legs were badly smashed and he was bleeding from the head."

"I tried to calm him down," Mullins added, "but all he could say was, 'What about my dog?' "

Pringle's black Labrador retriever, who was in the back of the car, escaped without injury.

Pringle is a 35-year veteran of the Royal Marines who became the commanding officer this year. He led a Marine commando unit on two tours of duty in Northern Ireland at the peak of sectarian violence there in the early 1970s, after earlier seeing action in Suez and Cyprus.

No one else was hurt in today's bombing, unlike last Saturday's explosion. Both persons killed by the explosion in Chelsea were passers-by: an elderly woman killed instantly by a six-inch nail flung through her heart by the homemade shrapnel bomb and an 18-year-old man who died days later. He was the son of an Irish immigrant.

Another bomb exploded in Northern Ireland today outside a golf club, but no one was injured. Terrorist violence has increased markedly in Northern Ireland since the recent end of the seven-month hunger strike by convicted Irish nationalist terrorists in the Maze Prison outside Belfast.

In addition to terrorist bombings of businesses in Ulster and military targets in London, Roman Catholic Irish nationalists and Protestant loyalist gunmen have escalated an exchange of retaliatory killings in working-class Catholic and Protestant ghettos in Belfast that have caused particular concern. The latest victims this week were an elderly Catholic woman, fatally shot by intruders as she slept in her bed, and a Protestant member of the militant Ulster Defense Association, killed outside his home by a gunman riding past on a motorcycle.

Police in Ulster and the Republic of Ireland said they believe the Provisional IRA also is responsible for the kidnapping yesterday of Ben Dunne, 32, son of the wealthy owner of about 70 department stores and supermarkets on both sides of the border in Ireland. A massive search is being carried out by Ulster and Irish police.

No ransom demand has been made yet, which a police spokesman in Dublin said was disturbing.

"The longer it goes on," he said, "the more worrying it becomes."