The man believed to have carried out the attack in Westminster has been named by police as Khalid Masood.
Kent-born Masood, who was shot dead in the attack, was not the subject of any current police investigations, but had a range of previous convictions.
The 52-year-old was believed to have been living in the West Midlands.
The so-called Islamic State group has said it was behind the attack, in which PC Keith Palmer, Aysha Frade and US tourist Kurt Cochran were killed.
Eight arrests – three women and five men – were made 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 also arrested at a separate 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.
Home Secretary Amber Rudd has told those gathered for a candlelit vigil in Trafalgar Square in central London 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 by police.