The attacker who killed three people near parliament in London before being shot dead was named on Thursday as British-born Khalid Masood, who was once investigated by MI5 intelligence officers over concerns about violent extremism.

The militant Islamic State (IS) group claimed responsibility for the attack in a statement issued by its Amaq news agency, but did not name Masood and gave no details. It was not clear whether the attacker was directly connected to the militant group.

Police said Masood, 52, was born in the county of Kent in southeast England and was most recently living in the West Midlands region of central England.

"Masood was not the subject of any current investigations and there was no prior intelligence about his intent to mount a terrorist attack," the Metropolitan Police said in a statement.

"However, he was known to police and has a range of previous convictions for assaults, including GBH (grievous bodily harm), possession of offensive weapons and public order offences."

Prime Minister Theresa May told parliament the attacker had once been investigated by the MI5 intelligence agency over concerns about violent extremism, but was a peripheral figure.

Police said Masood had never been convicted of a terrorism offence. His first conviction was in 1983 for criminal damage and his last one was in December 2003 for possession of a knife.

During five minutes of mayhem in the heart of London on Wednesday, Masood sped across Westminster Bridge in a car, ploughing into pedestrians. He then ran through the gates of the nearby parliament building and fatally stabbed an unarmed policeman before being shot dead.

Police arrested eight people at six locations in London and Birmingham in the investigation into the attack, which May said was inspired by a warped Islamist ideology.

The Enterprise rental car company said the vehicle used in the attack had been rented from its Spring Hill branch in Birmingham, which is located in the West Midlands.

"An employee identified the vehicle after seeing the license plate in an image online. We ran another check to verify, and immediately contacted the authorities," said company spokesman John Davies.

About 40 people were injured in the attack, of whom 29 remain in hospital, seven in critical condition.

May visited some of the wounded in hospital on Thursday, her spokesman said. She also chaired a meeting of the government's crisis response committee, and spoke to several leaders of countries whose nationals were caught up in the attack.

"Lone-wolf attack"

The bloodshed in London took place on the first anniversary of attacks that killed 32 people in Brussels, and resembled IS-inspired attacks in France and Germany where vehicles were driven into crowds.

The dead were Masood, two members of the public, and Keith Palmer, the 48-year-old policeman stabbed by Masood.

"He will be deeply missed. We love him so much," Palmer's family said in a statement. He was married with a five-year-old daughter.

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

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.

"My thoughts, prayers and deepest sympathy are with all those who have been affected by yesterday's awful violence," Queen Elizabeth said in a message.

US tourist Kurt Cochran was named as one of the dead in a Facebook post by family member Shantell Payne.

"With a heavy heart I must pass the sad news of our beautiful brother, father, husband, son and friend Kurt Cochran, he could not overcome the injuries he received in the London terror attacks," Payne wrote.

Her post said Cochran's wife, Melissa Payne Cochran, was in hospital with a broken leg and rib and a cut on her head.

US President Donald Trump paid homage to Cochran in a tweet, calling him "a great American".

A government minister was widely praised for trying to resuscitate Palmer, walking away from the scene with blood on his hands and face.

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

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

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

French Foreign Minister Jean-Marc Ayrault traveled to London to show solidarity and met some of the other students who were on the school trip and their families.

He told reporters the lives of the three youngsters were not in danger. Ayrault later attended the session in parliament where May spoke.