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”.
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”.
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.
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.