Seven people have been arrested in raids in London, Birmingham and elsewhere linked to the Westminster terror attack, police have revealed.
Mark Rowley, the Met's senior anti-terror officer, said six addresses were raided overnight.
He spoke as MPs were returning to Parliament in a show of defiance with a minute's silence to be held in Whitehall.
Defence Secretary Sir Michael Fallon told BBC Radio 4's Today programme the "working assumption" was that the attack was linked to "Islamic terrorism in some form".
Mr Rowley revised the death toll down from five to four - the attacker, Pc Keith Palmer, who he stabbed, and a woman in her mid 40s and a man in his mid 50s, who were mown down as the terrorist sped across Westminster Bridge in his car.
The woman was named in reports as Aysha Frade, a Spanish teacher who lived in London.
Mr Rowley said 29 people had been treated in hospital with seven people in a critical condition.
At the scene of one of the police raids, a flat in Hagley Road, Birmingham, one witness told the Press Association: "The man from London lived here."
Mr Rowley said it was still his belief the attacker worked alone and was inspired by "international terrorism", adding that there was no specific information to suggest any further threat to the public.
Speaking in the shadow of New Scotland Yard, yards from the site of Wednesday's atrocity, Mr Rowley said a "mix of nationalities" were among the dead.
He said: "Hundreds of detectives have been working through the night and during that time officers have searched six addresses and made seven arrests.
"The inquiries in Birmingham, London and other parts of the country are continuing."
The House of Commons and the House of Lords will sit at their normal times on Thursday, despite the parliamentary estate playing unwilling host to the attack the previous day.
Pc Palmer, 48, a father and husband, was an unarmed member of the Parliamentary and Diplomatic Protection Squad who had served for 15 years.
He was killed as he tried to stop the attacker at around 2.30pm on Wednesday.
The knifeman, who had left a trail of carnage on the bridge, was then shot dead by armed officers who swarmed into the courtyard where Pc Palmer died, just yards from the House of Commons, where MPs had gathered for Prime Minister's Questions earlier.
Theresa May praised the bravery of police officers, saying: "Any attempt to defeat those values through violence and terror is doomed to failure."
Stories of heroism and bravery emerged from the incident, which brought central London to a standstill and closed transport networks.
Paramedics fought to save Pc Palmer, and his attacker, on the floor of the cobbled courtyard in front of Parliament, with Foreign Office minister Tobias Ellwood among those who rushed to help.
Mr Ellwood, who lost his brother in the Bali bombing, could be seen pumping the officer's chest then standing above him, his hands and face smeared with blood.
A party of French schoolchildren were among those targeted on the bridge, while four students from Edge Hill University in Ormskirk were also hurt - two described as "walking wounded", and another couple said to have minor injuries.
Romanian and South Korean tourists were also caught up in the tragedy.
Mr Fallon said security arrangements at Westminster would be reviewed to look at whether current security arrangements are "adequate" and whether police at the front gates should be armed.
Mayor of London Sadiq Khan said a candlelit vigil will be held in Trafalgar Square on Thursday evening to "come together in solidarity to remember those who have lost their lives, to express sympathy with their families and loved ones and to show the world that we are more committed than ever to the values that we hold dear - that we remain united and open".
West Midlands Police first referred inquiries about the operation on Hagley Road to the Metropolitan Police, who refused to say whether it was connected with Wednesday's attack in Westminster.
But a witness who works nearby told the Press Association: "The man from London lived here."
Officers stormed a second-floor flat above a row of shops on Hagley Road at around 11pm last night, the witness said.
He added: "They came and arrested three men."
One of the flat's windows was covered in cardboard, with non-uniformed officers spotted taking pieces of equipment into the property.
As he was describing the events, the witness was interrupted by a police officer, who had been guarding the scene.
He had his details taken and was convinced to go to a police station with another officer.