Officers stormed a flat in Birmingham late on Wednesday night and at a separate addresses in the London area.
West Midlands Police directing inquiries about the operation to the Metropolitan Police.
The London force refused to comment on the raid’s connection to the bloody assault on Westminster, but one witness told the Press Association: “The man from London lived here.”
The House of Commons and the House of Lords will sit at their normal times today, despite the parliamentary estate playing unwilling host to the attack the previous day.
Pc Keith Palmer, a member of the Parliamentary and Diplomatic Protection Squad, was killed as he tried to stop the attacker at around 2.30pm on Wednesday, while two members of the public were also fatally injured.
The suspect, who was armed with two knives, injured around 29 people, seven critically, as he mowed down pedestrians with a car on Westminster Bridge before crashing at the railings in front of Parliament.
Bursting through the gate to the Palace of Westminster, he stabbed Pc Palmer before being shot dead by armed officers.
Theresa May praised the bravery of police officers on Wednesday night as it was announced Westminster would attempt to run as smoothly as normal.
In a statement from Downing Street, the Prime Minister said: “Any attempt to defeat those values through violence and terror is doomed to failure.
“(Thursday) morning, 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.”
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.”
Counter-terror detectives will continue searching for clues to how an armed attacker brought destruction to London.
Speaking outside Scotland Yard on Wednesday night, Acting Deputy Commissioner Mark Rowley, the Met’s senior anti-terror officer, said police believe the suspect was “inspired by international terrorism”, and they believe they know who he was.
Paying tribute to Pc Palmer, who had served the police for 15 years, Mr Rowley said: “Today in Westminster we saw tragic events unfold, and our thoughts are with those who lost loved ones, those who were injured and all those affected by this attack.
“One of those who died today was a police officer, Pc Keith Palmer, a member of our parliamentary and diplomatic protection command. Keith, aged 48, had 15 years’ service and was a husband and father.
“He was someone who left for work today expecting to return home at the end of his shift, and he had every right to expect that would happen.”
The attack has delayed the Queen’s planned visit to the new headquarters of the Metropolitan Police.
A Buckingham Palace spokesman said the decision had been taken to postpone the engagement in light of the attack.
Stories of heroism and bravery emerged from the incident, which brought central London to a standstill and closed transport networks around the capital shortly after 2.30pm on Wednesday.
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.
Armed officers, some in plain clothes and wearing balaclavas, swarmed around the yard feet from where MPs had earlier attended Prime Minister’s Questions.
The knifeman’s attack left a trail of destruction as paramedics tended to victims on the bridge and at the gate.
One woman hit by the attacker’s car before he reached Parliament was confirmed dead by a doctor at St Thomas’ Hospital. Others on the bridge suffered “catastrophic injuries”.
Another woman who fell into the Thames was rescued and given urgent medical treatment on a nearby pier.
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.