The Westminster attacker was British-born and known to the police and intelligence services, Prime Minister Theresa May has revealed.
She told MPs he had been investigated some years ago over violent extremism, but was “peripheral” and was not part of the current intelligence picture.
The so-called Islamic State group has said it was behind the attack.
Eight arrests in London and Birmingham followed Wednesday’s attack that left four dead – including the attacker.
Those killed by the attacker were PC Keith Palmer, Aysha Frade, who worked at a London college, and a man in his 50s.
Seven of the injured are still in hospital in a critical condition. A further 29 had been treated in hospital, police said.
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.
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.”
The so-called Islamic State claimed through its news agency that the Westminster attacker was a “soldier of the Islamic State”.
Westminster Bridge has now re-opened.
Mrs Frade worked at a London sixth form college just a few hundred metres from Westminster Bridge.
The 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 on their way home.
An emotional James Cleverly MP asked Mrs May to consider recognising posthumously the “gallantry and sacrifice” made by PC Palmer, who he knew from his time in the Army.
Analysis: The PM’s carefully-chosen words
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.
The BBC understands that searches and arrests have been carried out in Forest Gate, east London, Wales, Surrey and Sussex, as well as in Birmingham.
“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,” Mr Rowley said.
“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:
- The Queen has said her “thoughts, prayers, and deepest sympathy” are with all those who have been affected by the “awful violence”
- Security at Parliament will be reviewed, says Defence Secretary Sir Michael Fallon
- A candlelit vigil will be held in Trafalgar Square in central London on Thursday evening
- A JustGiving page, set up for the family of PC Palmer, has raised more than £25,000 so far
- The flag over the Houses of Parliament is flying at half mast
- MPs held a minute’s silence before Parliament continued business as normal
- The Pope said in a letter to the Archbishop of Westminster that he was “deeply saddened” and “assured the nation of his prayers”
- 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
Brendan Cox, the husband of murdered MP Jo Cox, said it was important to remember that “this was a story about people who didn’t come home yesterday”.
US President Donald Trump was among world leaders to offer their support to Mrs May, tweeting: “Spoke to UK Prime Minister Theresa May today to offer condolences on the terrorist attack in London. She is strong and doing very well.”
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