Twelve people have now been arrested as part of a widening terrorism investigation after three attackers used a van and large knives to turn a balmy London evening into a bloodbath with seven dead and scores injured.

Islamic State has claimed responsibility for Saturday night's attack on London Bridge and the nearby Borough Market, marking the third terrorist attack in the UK in three months and the second in two weeks.

British Prime Minister Theresa May says Britain must now toughen up on stamping out Islamist extremism and has proposed regulating cyberspace, adding that Britain has been far too tolerant of extremism.

"It is time to say, enough is enough," May said.

With the UK national elections due on June 8, the country's major political parties temporarily suspended campaigning but May says the vote will take place as scheduled because "violence can never be allowed to disrupt the democratic process."

The assault unfolded in a few terrifying minutes when a rented van veered off the road and ploughed into pedestrians on busy London Bridge. Three men then got out of the vehicle with large knives and attacked people at bars and restaurants in nearby Borough Market until they were shot dead by police.

"They went 'This is for Allah,' and they had a woman on the floor. They were stabbing her," one witness Gerard Vowls said.

Florin Morariu, a Romanian chef who works in the Bread Ahead bakery, said he saw people running and some fainting. Then two people approached another person and "began to stick the knife in ... and then I froze and I didn't know what to do."

He said he managed to get near one attacker and "hit him around the head" with a bread basket.
"There was a car with a loudspeaker saying 'go, go' and they (police) threw a grenade. ... and then I ran," he said.

London police said officers killed the attackers within eight minutes of arriving at the scene. Eight officers fired some 50 rounds, said Assistant Commissioner Mark Rowley, the force's head of counterterrorism.

Islamic State's statement from its Amaq news agency claimed the group's "fighters" were responsible, according to the SITE Intelligence Group. IS has urged supporters to weaponise vehicles in attacks against the West.

It was the third attack in Britain this year that Islamic State has claimed - after a similar attack on Westminister Bridge in March and the Manchester concert bombing two weeks ago - and one of several involving vehicles in Europe, including last year's Bastille Day rampage in the French city of Nice.

The three attackers Saturday were wearing what appeared to be suicide belts, but the belts turned out to be fake. Investigators were working to determine whether others assisted them, Rowley said.

A bystander was also wounded by the gunfire, but the civilian's injuries were not believed to be critical.

Forty eight people, including two police officers, were treated at hospitals. Twenty-one remained in critical condition on Sunday. Among the wounded were German, French and Spanish citizens, officials said.

Canadian Prime Minister Justin Trudeau said a Canadian was among the dead. A French national was also confirmed dead.

Counterterrorism officers raided several addresses in Barking, an east London suburb, and arrested 12 people there Sunday, police said.

Neighbours at the site of one raid in Barking said a man who lived there resembled one of the attackers shown in news photographs.

"He's lived here for about three years," Damien Pettit said. "He's one of our neighbours. I've said hello in passing more than 50, 60 occasions. He has two young kids. He was a very nice guy."

Britain's official terrorism threat level was raised from "severe" to "critical" after the Manchester attack, meaning an attack may be imminent. Several days later it was lowered again to "severe," meaning an attack is highly likely.