Police have identified Khalid Masood as the man who carried out the Westminster attack, as the death toll rose to five.
Masood, 52, was born as Adrian Elms in Kent and was shot dead by police. He had not been the subject of any current police investigations.
PC Keith Palmer, 48, Aysha Frade and US tourist Kurt Cochran, 54, were killed on Wednesday, while a 75-year-old man died on Thursday evening.
The so-called Islamic State group has said it was behind the attack.
Three women and five men were arrested in London and Birmingham on suspicion of preparation of terrorist acts following Wednesday's attack.
- A woman aged 39 was arrested in east London
- 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 another address in Birmingham
- A man aged 58 was arrested at an address in Birmingham
The Met Police says detectives are continuing to search a number of addresses, including one in Carmarthenshire, three in Birmingham and one in east London. Addresses in Brighton and south-east London have also been searched.
'We will defeat them'
Home Secretary Amber Rudd told those gathered for a candlelit vigil in London's Trafalgar Square on Thursday evening that terrorists "will not win".
"We are all connected and today we showed that by coming together, by going to work, by getting about our normal business, because the terrorists will not defeat us. We will defeat them," she said.
Masood drove into pedestrians on Westminster Bridge before crashing his car into railings and then running into the grounds of Parliament, armed with a knife.
He stabbed PC Palmer before being shot dead.
The Metropolitan Police said there had been no prior intelligence about Masood's intention to carry out an attack.
But he was known to the police and his previous convictions included causing grievous bodily harm, possession of offensive weapons and public order offences. He was believed to have been living in the West Midlands.
Masood is believed to have lived at various times in Crawley, West Sussex, and Rye and Eastbourne, both in East Sussex.
He also appears to have been convicted of a knife crime in 2003 in Eastbourne.
His first conviction was in November 1983 for criminal damage and his last in December 2003 for possession of a knife.
He had not been convicted of any terrorism offences.
Car hire company Enterprise said the vehicle used in the attack had been rented from its Spring Hill depot in Birmingham.
The BBC understands Masood hired the Hyundai SUV in person, giving his profession as a teacher.
The Department for Education said it had no record of him having worked as a qualified teacher in English state schools.
It appears that he styled himself as an English tutor at one point.
At the Trafalgar Square vigil
By Jodie Halford, BBC News
People gathered in Trafalgar Square stood together quietly, flanked by police officers with the sound of helicopters a constant presence above.
The people of London and visitors to the city came together to remember the people who lost their lives in Wednesday's attack. The word "solidarity" was heard over and over again.
Candles were laid on the floor and on the steps leading to the National Gallery, waiting to be lit in memory of those who died.
As the bells of St Martin's in the Fields chimed, the crowds fell silent and paused to think about Wednesday's events.
Some filmed the scene on their phones, some cast glances across the crowds, but the focus was on the candles on the steps leading up to the National Gallery, above which MPs, religious figures and others stood in a line to pay their respects.
PC Palmer, who was stabbed in the grounds of Parliament, was a father.
He was an unarmed member of the parliamentary and diplomatic protection squad, with 15 years' service.
His family said in a statement that he would be remembered as a "wonderful dad and husband".
'Brave and courageous'
They also described him as "a loving son, brother and uncle. A long-time supporter of Charlton FC. Dedicated to his job and proud to be a police officer, brave and courageous. A friend to everyone who knew him.
"He will be deeply missed. We love him so much.
"His friends and family are shocked and devastated by his loss and ask that they are left to grieve alone in peace."
A JustGiving page set up for the family of PC Palmer reached its initial target of £100,000 on Thursday afternoon, less than 24 hours after it had been set up.
The amount pledged has now passed £320,000, after the target was raised several times.
The Met said that as a mark of respect, the constable's shoulder number, 4157U, would be retired and not reissued to any other officer.
Mrs Frade worked at a London college, while Mr Cochran was from Utah, in the US, and had been visiting the capital with his wife Melissa, who is in hospital with serious injuries.
According to a family statement, the Cochrans had been celebrating their 25th wedding anniversary and were due to return to the US on Thursday.
Mrs Frade and Mr Cochran were killed on Westminster Bridge.
Mrs Frade worked at a London sixth-form college, just a few hundred metres from the bridge.
The principal at DLD College, Rachel Borland, said she was "highly regarded and loved by our students and by her colleagues".
In other developments:
- The Queen said her "thoughts, prayers, and deepest sympathy" were with those affected by the "awful violence"
- MPs held a minute's silence before Parliament continued business as normal
- Prime Minister Theresa May spent 40 minutes visiting the injured in hospital
- 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
Police have said five people remain in a critical condition in hospital and two have life-threatening injuries.
A total of about 40 people had been treated in hospital, police said.
A Romanian couple injured in the attack have been identified as Andrei Burnaz and Andreea Cristea. The Romanian embassy in London has confirmed that Ms Cristea is the person who fell from Westminster Bridge during the attack.
The casualties also included 12 Britons, three French children -who have since returned home -, four South Koreans, one German, one Pole, one Irish, one Chinese, one Italian, one American and two Greeks.
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