It was not immediately clear whether the London police knew that MI5 had looked into Mr. Masood.
Before Mrs. May spoke, the secretary of state for international trade, Liam Fox, began taking questions on trade issues by stating that it would be “not violence, hatred or division, but decency, goodness and tolerance that prevails in our country.”
Speaking outside the chamber, Ed Miliband, a former leader of the Labour Party, said that the mood had been one of “shock and determination, and also admiration for the job that the security people are doing.”
The reaction, he added, showed that “humanity is stronger than the cowardice and depravity of the person who did this.”
Signs of the chaos from the day before were still in evidence. In the area where the fatal stabbing took place, just inside the gates of Parliament, a small blue tent had been erected over the site of the crime scene as the police continued forensic and other investigations.
The area around Parliament Square remained cordoned off, and a fire truck with flashing lights could be seen parked outside the Palace of Westminster, while parts of two of London’s main roads — Whitehall and Millbank — were off limits. The security cordon extended to Trafalgar Square, covering the entirety of Whitehall, the heart of Britain’s government, including the prime minister’s office, the Finance Ministry and the Foreign Office.
Runners and cyclists took detours, while employees of Parliament and government ministries, including the Ministry of Defense, were allowed through the cordon only after identification checks by the police.
Large thoroughfares typically packed with traffic during the morning rush hour were largely deserted, with roads like the Mall, which connects Trafalgar Square to Buckingham Palace, being used only by bicycles.
Among those headed to work was Michael Torrance, 39, a House of Lords official. Clutching a box of tea bags in his hand — his office had quickly run out as politicians and their staff members were on lockdown the day before — Mr. Torrance said that the full magnitude of the attack on the Parliament area had not yet sunk in.
“Everyone was in various states of shock,” he said. “Looking at it in context, up and until the late ’70s, it was a frequent target of I.R.A. attacks.”
“Without sounding too fatalistic,” he added, “there was an air of inevitability about some kind of incident like this happening eventually.”
He continued, “Parliament is obviously an iconic British institution, everyone was concerned, knew it was a target. Everyone’s alive to that.”
Mr. Torrance noted that “everyone wanted to be as normal as possible,” and that sentiment seemed to be shared across the city early Thursday morning, as Londoners went to work as usual. Many clutched newspapers, with lurid headlines and photographs detailing the bloody attack.
Mrs. May said in a speech on Wednesday that life would go on and that the country must not cave into terrorism, and Londoners seemed to be taking the attacks in stride.
“As I was coming in through the Tube, I noticed there was a great air of calm,” said Elizabeth Sweeney, 57, who works at the European Parliament and was in London at the time of the attack. “That was the overriding sense that I had, first thing.”
After the recent bloody attacks in Brussels and Paris, many Londoners shared a sense of inevitability that the British capital could be next. They said that expectation, combined with British mettle conditioned over centuries of war, terrorism and other challenges, had helped people stay calm.
“We do have a tendency to just get on with it,” said Meredith O’Shaughnessy, 38, an event planner.
“It takes a lot to shake a Londoner. The Blitz spirit lives on,” she added, referring to the German raids over Britain during World War II, when Britons — and Londoners — showed determination and resolve.
At least three police officers were among those wounded on the bridge. Also among the wounded were three 10th-grade boys from a group of students visiting from the Brittany region of France, and a woman who fell or plunged into the River Thames. A spokeswoman for the Paris prosecutor’s office said on Thursday that because three of the victims were French, it had opened an investigation into attempted murder in relation to a terrorist enterprise.
Law enforcement officials said that the police were now focused on analyzing the background and the motive of the attacker. Roy Ramm, who spent nearly three decades in the Metropolitan Police and was the commander of specialist operations, said that once officers had identified the attacker, they would move backward, using closed-circuit TV footage to track his movements throughout the day.
Mr. Ramm said that another team would simultaneously be researching the assailant’s background and those of his associates, and would see if he had ever been the subject of surveillance or on watch lists.
Mr. Ramm added that British intelligence authorities would be communicating with their international counterparts to establish whether the suspect was part of a network, and also to determine if he was on their radar at all, had left a travel footprint, or was known to have associated with known radical individuals.
Mr. Ramm said the violence showed how a so-called “marauding terrorist” could execute a “low-tech” assault. “There were no guns to purchase on a risky illicit market, no explosives to obtain or synthesize,” he said.
The attack brought to mind Islamic State attacks using vehicles in Berlin and in Nice, France, although the toll in London was far lower. Part of the investigation in London, law enforcement officials said, would focus on the car the assailant used, a Hyundai Tucson, which has already offered some clues: It was registered in Chelmsford, to the east of London, and may have been rented in Birmingham, one of the places the police conducted raids overnight.
Mr. Ramm said that the vehicle would undergo a major forensic examination, including checks for fingerprints and DNA to identify anyone else who might have been in the vehicle. “This is a lot of work and a big test,” he said.
Questions were already being raised as to how a knife-wielding attacker had been able to get so close to the Houses of Parliament, the center of British democracy. Several lawmakers asked how the assailant had been able to enter the area below the iconic clock tower known as Big Ben, and called for the security gaps to be plugged.
Britain has one of the most sophisticated counterterrorism operations in Europe, but efforts to track extremists have become harder in recent years, experts say. For years, the police were able to keep close tabs on potential Islamist radicals and terrorists, including Anjem Choudary, one of the most outspoken and effective hate preachers in Britain. For years he was the public face of radical Islam, encouraging dozens of followers to travel to Syria to join the Islamic State and vowing to convert Buckingham Palace into a mosque.
The Home Office made support for the Islamic State a criminal offense in June 2014, when Mrs. May was home secretary, and experts on radicalism said that drove many Islamist extremists underground.
Mobeen Azhar, who has made several documentaries on Islamist radicalism in Britain and who knows Mr. Choudary, said that criminalizing support for the militant group had undoubtedly prevented some vulnerable young people from coming under the influence of radical propaganda. But he added that the networks had also become more careful, to avoid detection.
“It used to be that radicals in London would meet in church halls or at takeaways in East London, or set up stalls in parks,” Mr. Azhar said. “Now these networks meet in white vans and spaces not known to police, and have gone more underground, making them more difficult to track.”