The Westminster attacker was British-born and known to the police and intelligence services, the prime minister has revealed.
In a statement to the Commons, Theresa May said he had been investigated some years ago over violent extremism but had been a “peripheral figure”.
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“He was not part of the current intelligence picture,” she said.
Eight arrests have been made following the attack on Wednesday that left four dead.
Those that died are PC Keith Palmer, Aysha Frade who worked at a London college, a man in his 50s and the attacker.
Seven of the injured are still in hospital in a critical condition.
A further 29 had been treated in hospital, Mr Rowley added.
In the attack on Wednesday afternoon, a man drove a car along a pavement on Westminster Bridge knocking down pedestrians, creating panic and leaving dozens injured.
He then ran towards Parliament where he stabbed PC Palmer who was unarmed. Armed police then shot dead the attacker in the grounds.
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Mrs May paid tribute to PC Palmer saying: “He was every inch a hero and his actions will never be forgotten.”
She also said one of three police officers injured as they returned from an event to recognise their bravery was in a stable condition.
She told MPs, many of whom had been caught up in the commotion: “We will never waver in the face of terrorism.”
Mrs Frade worked at a London sixth form college just a few hundred metres from Westminster Bridge.
Principal at DLD College, Rachel Borland, said she was “highly regarded and loved by our students and by her colleagues”.
Mrs May said 12 Britons were admitted to hospital and other victims included three French children, two Romanians, four South Koreans, one German, one Pole, one Irish, one Chinese, one Italian, one American and two Greeks.
Thierry Terret, who is in charge of schools in Brittany, said the three injured students were not in a life threatening condition and were expected to be back home by Friday.
By Dominic Casciani, home affairs correspondent
The prime minister’s carefully-worded statement that the killer was once investigated raises more questions than it currently answers.
It appears that the individual was discounted as a “peripheral figure” on the edge of some other operation. She didn’t say whether that means he was considered and discounted for good reason by MI5 intelligence officers, investigated for a criminal offence by detectives or even ever arrested.
However, she also stressed he was not part of the “current intelligence picture” – and that means he wasn’t currently on the radar at all. This points to the very difficult dilemma faced by security services combating these kinds of threats.
Every day they have to prioritise, or triage, who to pursue and who to discount. People who were once a threat change their thinking. They grow up, have kids and settle down. MI5, meanwhile, is tasked with focusing on those they know of with the most advanced plans.
Some of those they discount, or temporarily turn away from, later turn out to be more dangerous that initially thought. They include the ringleader of the 7/7 bombings and one of the two men who killed Fusilier Lee Rigby.
Intelligence is never a complete picture – it is not even like a jigsaw with missing pieces. It’s a case of trying to interpret fragments of information that rarely amount to a whole.
In a statement made earlier outside Scotland Yard, Acting Deputy Commissioner Mark Rowley said seven arrests had been made during raids in London and Birmingham – an eighth was announced several hours later.
“It is still our belief – which continues to be borne out by our investigation – that this attacker acted alone and was inspired by international terrorism.
“To be explicit, at this stage we have no specific information about further threats to the public.”
He urged journalists not to publish the attacker’s name while searches were continuing.
He said Londoners should expect to see more police officers on the streets, after officers’ leave had been cancelled and duty hours extended.
It was initially thought that three members of the public had been killed on Westminster Bridge, but Mr Rowley referred to just two in his statement.
Director General of MI5 Andrew Parker condemned the attack as “appalling and disgusting”.
The agency’s operational response was “fully mobilised in support of the police”, he said.
In other developments:
- A witness told the Press Association that three men were arrested in an armed raid on a Birmingham address. The BBC understands this is linked to the London attack
- Security at Parliament will be reviewed, says Defence Secretary Sir Michael Fallon
- The flag over the Houses of Parliament is flying at half mast
- MPs held a minute’s silence before Parliament continued business as normal
- People worried about family and friends can call the police casualty bureau on: 0800 056 0944 or 0207 158 0010. Anyone with images or footage of the incident can send them to ukpoliceimageappeal.co.uk
Defence Secretary Sir Michael Fallon told BBC Radio 4’s Today programme the “working assumption” was that the attack was linked to “Islamic terrorism in some form”.
He paid tribute to Pc Palmer, a 48-year-old father and husband, and an unarmed member of the Parliamentary and Diplomatic Protection Squad who had served for 15 years.
Pc Palmer stopped the attacker getting into Parliament and “gave his life for the democracy we all cherish”, he told BBC Breakfast.
Asked about the mood of the city, Sir Michael said: “London is getting back to normal. They’ve seen terrorism like this before and they are not going to let it triumph.”