The attacker who killed three people near the British Parliament before being shot dead was British-born and was once investigated by MI5 intelligence agents over concerns about violent extremism, Prime Minister Theresa May said today.

Police arrested eight people at six locations in London and Birmingham in the investigation into yesterday's lone-wolf attack that May said was inspired by a warped Islamist ideology.

Forty people were injured and 29 remain in hospital, seven in critical condition.

The assailant sped across Westminster Bridge in a car, ploughing into pedestrians along the way, then ran through the gates of the nearby Parliament building and fatally stabbed an unarmed policeman before being shot dead.

"What I can confirm is that the man was British-born and that some years ago he was once investigated by MI5 in relation to concerns about violent extremism," May said in a statement to Parliament.

"He was a peripheral figure...He was not part of the current intelligence picture. There was no prior intelligence of his intent or of the plot," she said, adding that his identity would be revealed when the investigation allowed.

Westminster Bridge and the area just around Parliament were still cordoned off this morning and a line of forensic investigators in light blue overalls were on their hands and knees, examining the scene where the attacker was shot.

The dead were two members of the public, the stabbed policeman and the attacker.

It was the worst such attack in Britain since 2005, when 52 people were killed by militant islamist suicide bombers on London's public transport system. Police had given the death toll as five but revised it down to four today.

The casualties included 12 Britons, three French children, two Romanians, four South Koreans, one German, one Pole, one Chinese, one American and two Greeks, May said.

"We meet here, in the oldest of all parliaments, because we know that democracy and the values it entails will always prevail," she said.

"A terrorist came to the place where people of all nationalities and cultures gather what it means to be free and he took out his rage indiscriminately against innocent men, women and children," said May.

A minute's silence was held in parliament and in front of police headquarters at New Scotland Yard at 0933 GMT, in honour of the victims - 933 was the shoulder number on the uniform of Keith Palmer, the policeman who was stabbed to death.

'Things from daily life'

Some have been shocked that the attacker was able to cause such mayhem in the heart of the capital equipped with nothing more sophisticated than a hired car and a knife.

"The police and agencies that we rely on for our security have forestalled a large number of these attacks in recent years, over a dozen last year," said Defence Minister Michael Fallon.

"This kind of attack, this lone-wolf attack, using things from daily life, a vehicle, a knife, are much more difficult to forestall," he told the BBC.

Three French high-school students aged 15 or 16, who were on a school trip to London with fellow students from Brittany, were among the injured.

French Foreign Minister Jean-Marc Ayrault, who travelled to London to bring a message of solidarity, met some of the other students who were on the school trip and their families at a hotel near the hospital where the injured were being treated.

He told reporters the lives of the three youngsters were not in danger. Ayrault later attended the session in parliament where May spoke. France has been hit by repeated deadly Islamist attacks over the past two years.

A vigil was planned in London's Trafalgar Square at 6pm.

A meeting of COBR, the government's crisis response committee, was due to take place later today morning.

Anti-immigration groups were quick to make links between immigration and the attack, though it was subsequently revealed the attacker was British-born.

Leave.EU, a group that has campaigned for immigration to be severely restrained as part of Britain's exit from the European Union, accused mainstream politicians of facilitating acts of terror by failing to secure borders.

In France, far-right presidential candidate Marine Le Pen also drew a link, saying that events in London highlighted the importance of protecting national borders and stepping up security measures.

The Scottish parliament, which suspended a planned debate and vote on independence yesterday because of events in London, was due to resume those proceedings on Tuesday, the BBC reported.

- Reuters