Four people have died, including a police officer and the attacker.
Police say 29 other people were treated in hospital, seven of whom are in a critical condition.
The assailant was named by police on Thursday as Khalid Masood, 52, who was born in Kent but was believed to have been living in the West Midlands most recently.
He drove a car into pedestrians on Westminster Bridge, killing two people, before crashing it outside parliament and trying to enter the complex armed with two knives.
London terror attack: 75-year-old man becomes fourth victim – as it happened
Police name Khalid Masood, 52, born in Kent as man responsible for attack in which three victims have died and seven more are critically injured
He stabbed an unarmed police officer who later died from the injuries. Armed police then shot the attacker. The police officer was identified as PC Keith Palmer, 48, who had 15 years of service with the parliamentary and diplomatic protection service and was a husband and father.
Another victim was named as Aysha Frade, 43, who worked at a sixth-form college in Westminster. The mother of two had family in Betanzos, Galicia, north-west Spain, and her death was confirmed by the mayor of the town.
The third person killed by the attacker was named as Kurt Cochran, a tourist from Utah in the US. He and his wife, Melissa, were on the last day of a trip to Europe to celebrate their 25th wedding anniversary. Melissa remains in hospital with serious injuries.
The prime minister, Theresa May, said the attacker had been investigated “some years ago” by MI5 in relation to concerns about violent extremism but was “not part of the current intelligence picture”.
The Metropolitan police said Masood had a range of previous convictions for assaults, including GBH, possession of offensive weapons and public order offences. His most recent was in December 2003 for possession of a knife.
Islamic State claimed responsibility for the attack. It released a statement through the Amaq news agency, which it uses to broadcast propaganda, calling the attacker “a soldier of Islamic State”. The claim is unverified.
The attacker is believed to have acted alone but police are investigating possible associates. May said there was no reason to believe further attacks on the public were planned.
Police have searched six addresses in Birmingham, London and other parts of the country. Five men and three women were arrested on suspicion of preparation of terrorist acts.
Theresa May told MPs in a statement to parliament on Thursday: “We are not afraid and our resolve will never waver in the face of terrorism.” The prime minister, who was evacuated from parliament within minutes and driven to Downing Street, described Palmer as “every inch a hero”.
Twelve Britons were injured, including three police officers, two of whom were seriously injured. Four university students, three French children, four South Koreans, two Romanians, two Greeks, a Chinese national, an Italian, an American, a Pole, an Irish national and a German woman resident in Australia were also hurt.
A Romanian tourist pulled from the Thames was celebrating her boyfriend’s birthday in London. She sustained serious head injuries and badly damaged lungs, while her boyfriend suffered a fractured foot. The Romanian embassy in London confirmed the woman’s name as Andreea Cristea.