The so-called Islamic State group has said it was behind the attack on British Parliament house,m even as eight persons have been arrested over the attack.
The arrests in London and Birmingham followed the attack that left four dead – PC Keith Palmer, Aysha Frade, Kurt Cochran and the attacker.
Ms Frade worked at a London college, while Mr Cochran was from Utah, in the US, and visiting the capital with his wife Melissa, who is in hospital with serious injuries.
According to a family statement, the couple were celebrating their 25th wedding anniversary and were due to return to the US on Thursday.
PC Palmer was a 48-year-old father, who was an unarmed member of the Parliamentary and Diplomatic Protection Squad, with 15 years’ service in the force.
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. Armed police 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.”
Westminster Bridge has now re-opened.
Image caption PC Keith Palmer stopped the attacker in his tracks. Aysha Frade would be deeply missed by all, the principal at the college said
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.