Khalid Masood, 52, mowed down pedestrians on Westminster Bridge before charging through the gates of parliament wielding two knives and stabbing a policeman to death.
PC Keith Palmer, Aysha Frade and US tourist Kurt Cochran were killed on Wednesday. A 75-year-old man died yesterday evening. The man had been receiving medical treatment in hospital but his life support was withdrawn.
It was also reported last night that police performed a controlled explosion near Westminster, less than a mile away from the scene of the attack.
The Metropolitan Police said that officers found an unattended bag in Birdcage Walk, between Westminster and Buckingham Palace.
Yesterday, as police mounted a UK-wide anti-terrorist operation and forensics officers combed the crime scene inside the gates to New Palace Yard, MPs and staff returned to work in a show of defiance that terrorism would not halt democracy. But there was a sombre mood to proceedings as the Prime Minister led tributes to the victims, in particular Mr Palmer, the 48-year-old father and husband who lost his life in the line of duty.
A nationwide minute of silence was observed at the start of Westminster parliamentary business. Last night a candle-lit vigil was held in Trafalgar Square attended by London mayor Sadiq Khan and Home Secretary Amber Rudd.
Downing Street said Theresa May spent 40 minutes yesterday afternoon visiting some of those injured in the attack, and that she signed a book of condolence.
Addressing the Commons earlier, she vowed that terrorists “would not defeat us” and said the UK “will never waver in the face of terrorism”.
“The greatest response lies not in the words of politicians, but in the everyday actions of ordinary people,” she said. “Let this be the message from this House and this nation today. Our values will prevail.”
In her Commons statement, Mrs May also said that police together with the House authorities were reviewing the security of the parliamentary estate.
Labour leader Jeremy Corbyn issued a call “not to rush to judgment” and to “stay united in our communities and not allow fear or the voices of hatred to divide or cower us”.
Paying tribute to Mr Palmer, Mrs May said: “He was every inch a hero and his actions will never be forgotten.”
She went on to praise the police for “heroically” stopping the attacker.
“We should be clear first of all that an attacker attempted to break into parliament and was shot dead within 20 yards of the gate,” the Prime Minister said. “If his intention was to gain access to this building, we should be clear that he did not succeed.”
It emerged that three of the 29 people hospitalised are police officers who were returning from a ceremony to recognise their bravery. Two of them are said to be in a serious condition.
The injured are citizens of 11 nations, with those admitted to hospital including 12 Britons, three French children, two Romanians, four South Koreans, one German, one Pole, one Irish, one Chinese, one Italian, one American and two Greeks.
The Prime Minister told MPs that Masood had been known to the security services for extremist activities but was a “peripheral” figure who was “not part of the current intelligence picture”.
Mrs May said MI5 had investigated Masood “some years ago” but that there was “no prior intelligence of his intent or of the plot”.
In a post on the website used to claim responsibility for previous attacks, the IS terrorist group said Masood was one of its “soldiers”.
In reference to the fight to defeat IS in Syria and Iraq, the statement said: “The attacker yesterday in front of the British Parliament in London was a soldier of the Islamic State executing the operation in response to calls to target citizens of coalition nations.”
Police confirmed that Masood, born in Kent but believed to be living in the West Midlands, had criminal convictions including for assault and possession of a knife.
It was reported that the rental form for the car used in the attack listed his occupation as an English teacher.
Counter-terrorism officers raided six properties across the UK and arrested eight people on Wednesday night and yesterday morning. Addresses in Birmingham, Brighton. Carmarthenshire and south-east London were searched.
A 39-year-old woman was arrested in east London, while a 21-year-old woman and a 23-year-old man were arrested in Birmingham. A 26-year-old woman and three men aged 28, 27 and 26 were arrested at a separate address in Birmingham.