Police have arrested seven people in connection with the terror attack that brought bloodshed to the heart of London.
The Metropolitan Police's top anti-terror officer confirmed police have searched six addresses and made seven arrests.
Defence Secretary Sir Michael Fallon told BBC Radio 4's Today programme the "working assumption" was the attack was linked to "Islamic terrorism in some form".
The black-clad terrorist, armed with two knives, mounted the pavement on Westminster Bridge and mowed his car through a crowd of people, including schoolchildren.
He was then shot dead by armed officers in the courtyard outside the Houses of Parliament after he stabbed Pc Keith Palmer, who died of his wounds.
Speaking in the shadow of New Scotland Yard, yards from the site of the atrocity, the Met Police's acting deputy commissioner Mr Rowley 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."
He said: "They have been working right through the night, looking into his background, how he got hold of the vehicle, where the vehicle has been in the last day or two, and who may, or may not, have helped him."
Asked if he was known to police, Sir Michael said: "I can't confirm that, you will have to ask the police that."
Mr Rowley revised the death toll down from five to four, but said a "mix of nationalities" were among the dead.
PC Keith Palmer, a member of the Parliamentary and Diplomatic Protection Squad, was stabbed to death as he tried to stop the attacker inside the grounds of the Houses of Parliament.
Two members of the public, one believed to be a Spanish teacher on her way to pick her children up from school, the other a man in his 50s, were also killed in the attack.
Aysha Frade, 43, died of her injuries after the attacker ploughed his car into pedestrians on Westminster Bridge.
Spanish media said Mrs Frade had two daughters aged eight and 11 and worked at the nearby DLD College London.
The terrorist was shot three times by armed police and later pronounced dead in hospital.
Mr Rowley said 29 people had been treated in hospital with seven people in a critical condition.
Speaking as MPs were returning to Parliament in a show of defiance, he said: "We must not allow terrorists to create discord, distrust and fear.
"The police stand with all communities, later today a meeting of faith leaders will be held here at New Scotland Yard.
"Whilst our work to investigate and understand what happened yesterday continues with vigour, we must also reflect.
"I want to thank the public for their support and all their good wishes, I know it is appreciated by all those men and women who are out there today protecting us."
Sir Michael Fallon said police were investigating whether the attacker acted alone or had help.
The Defence Minister told BBC Radio Four's Today programme: "It was no accident that this attack was on Westminster, because it is at Westminster that we debate differences, very sharp differences, very freely and respectfully between us, and this kind of Islamic terrorism doesn't respect those differences, so it is no accident that there was an attack here."
He went on to praise the police response: "They have been working right through the night, looking into his background, and how he got hold of the vehicle, where the vehicle has been in the last day or two, and who may, or may not, have helped him."
Asked if the attacker was known to police, he said: "I can't confirm that, you will have to ask the police that."
Sir Michael said a spirit of defiance was the best response to such attacks.
"It is also, I think, evident form everyone involved yesterday that we are not going to let this kind of terrorism win."
Britain's most senior police officer witnessed the terror attack at Westminster.
Acting commissioner of the Met Police Craig Mackey is being treated as a significant witness as he was on the scene.
Speaking outside Scotland Yard just yards from the scene of the attack, Mr Mackey said: "I personally was a witness to part of yesterday's events, including part of the tragic attack on Pc Palmer.
"As with all police officers, I therefore had a duty to secure my evidence and produce statements yesterday evening, which I did before resuming my role leading our response to this incident."
Prime Minister Theresa May praised the bravery of police officers as it was announced that the Houses of Commons and Lords would run as normal the day after the attack.
"Any attempt to defeat those values through violence and terror is doomed to failure,” she said.
"Parliament will meet as normal. We will come together as normal.
"And Londoners, and others from around the world who have come here to visit this great city, will get up and go about their day as normal.
"They will board their trains, they will leave their hotels, they will walk these streets, they will live their lives.
"And we will all move forward together, never giving in to terror and never allowing the voices of hate and evil to drive us apart."
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, with 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.
Donald Trump was among world leaders to offer their support.
Shortly after 1.30am UK time, the US president tweeted: "Spoke to UK Prime Minister Theresa May today to offer condolences on the terrorist attack in London. She is strong and doing very well."
