Police have arrested eight 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 had searched six addresses and made seven arrests, and the Met later released a tweet to say they had made an eighth arrest.
Isis claimed responsibility for the attack via its Amaq news agency.
Addressing the Commons, Prime Minister Theresa May said: "We are not afraid and our resolve will never waiver in the face of terrorism."
Ms May said the attacker was a British citizen who was known to police and security services, and had been investigated some years ago over violent extremism. She said the working assumption was he was inspired by Islamist terrorism.
She told MPs: "Yesterday an act of terrorism tried to silence our democracy, but today we meet as normal, as generations have done before us and as future generations will continue to do, to deliver a simple message: 'We are not afraid and our resolve will never waver in the face of terrorism'."
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."
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."
The Queen sent her condolences to those affected: "My thoughts, prayers, and deepest sympathy are with all those who have been affected by yesterday's awful violence."
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."
The head of MI5 has condemned the attack as "appalling and disgusting".
Andrew Parker, director-general of the security service, confirmed its operational response has been "fully mobilised".
He said in a statement: "The thoughts of the men and women of MI5 are with the families of those killed in Westminster yesterday, and with the other innocent people injured in this appalling and disgusting attack.
"We stand shoulder to shoulder with our police colleagues, grieving at their loss while also applauding the professional excellence of their response.
"As Acting Deputy Commissioner Rowley said, the security community prepares for such awful events — while working tirelessly to prevent them.
"The MI5 operational response is fully mobilised in support of the police."
Britain's most senior police officer confirmed he 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."