Kirsten Hurrell, 70, who owns a newsstand opposite Big Ben, said she had seen a car swerve across a bicycle lane and into a fence around Parliament. She saw a body lying on the ground and called emergency services. “At first I thought it was an accident, but then I was told the car had already mowed down quite a number of people on Westminster Bridge,” she said, adding: “Now that it is a terrorist incident, it is a bit more daunting.”

Robert Vaudry, 52, a fund manager from Stratford-upon-Avon, said he had emerged from the Westminster subway station around 2:40 p.m. for a meeting with a lawmaker when he realized that something was amiss.

“I came out of the Tube and there were two armed policemen,” he said in an interview. “One grabbed my arm, pushed me to the left and said, ‘Get out of here,’” he said. “They were shouting at everyone to get away.” As he spoke, police officers were cordoning off the area. One officer shouted, “We need everyone to move back past Downing Street.”

Radoslaw Sikorski, a former foreign minister of Poland who was in the area, was in a taxi on Westminster Bridge when the pedestrians were hit by the other vehicle. “I didn’t see the impact, I heard it — it sounded like a car hitting a sheet of metal,” he said. “I saw these people lying on the tarmac, on the pavement. I saw five people down, one unconscious and one bleeding heavily from his head. He was not moving. The taxi driver rang the emergency services, and people rushed to help.”

Andrew Bone, the executive director of the Responsible Jewellery Council, an industry standards group, was on a bus heading toward Victoria Station when it was stopped at the edge of Parliament Square. Seeing the commotion, he initially thought an action movie was being shot, but quickly discerned the gravity of the situation as the bus was evacuated and he saw the vehicle that had crashed into a railing.

“We had a front-row seat as the first responders arrived,” Mr. Bone said. “I am of the generation who remembers I.R.A. bombs in London during the Troubles,” he said, referring to the sectarian conflict in Northern Ireland. “We are not indifferent, but police have reacted with calm. I saw no panic.”

Britain has not suffered a large-scale terrorist attack since July 7, 2005, when bomb attacks on subway trains and on a bus killed more than 50 people. Political violence is relatively rare in Britain, where gun ownership is stringently restricted.

Jo Cox, a Labour member of Parliament, was assassinated in her constituency in northern England on June 16, a week before the contentious referendum on whether Britain should leave the European Union.

In 1979, a lawmaker was assassinated near the Parliament building. Airey Neave, a Conservative Party member, was killed when his car was blown up.

Jeremy Shapiro, a former State Department official now at the European Council on Foreign Relations, said that the London attack was consistent with the recent pattern of attacks in which a vehicle was used to kill people, citing assaults in France, Germany and Israel.

“We’ve seen a gradual movement away from terrorist attacks on the West to attacks on softer and softer targets with more improvised weapons,” he said. “In a way, it’s a sign of desperation and a demonstration of the effectiveness of counterterrorism in the West. It’s spectacularly easy to kill a bunch of people with a car or a truck if you don’t care who they are.”