The next moment, a vehicle is captured on CCTV camera tearing across the bridge on the footpath, travelling at more than twice the speed of the surrounding traffic.

In a disturbing scene, a small, dark figure is then shown plummeting from the bridge deck and splashing into the River Thames, about six metres below.

That figure was a woman, who authorities have confirmed was pulled alive from the River Thames in the wake of a terror attack that left five people dead and at least 40 others wounded on Wednesday afternoon, local time.

British authorities said the attacker deliberately ploughed his Hyundai into pedestrians on the bridge, before fatally stabbing a police officer outside the British Houses of Parliament. The attacker was then shot and killed.

The footage, obtained by the BBC, was captured on a CCTV camera south of the bridge, from a considerable distance away. It is unclear whether the woman jumped from the bridge to escape the speeding vehicle, or whether the impact propelled her over the side.

The unidentified woman was pulled onto a pier and treated for serious injuries, The London Port Authority said.

"A female member of the public was recovered from the water near Westminster Bridge," a Port Authority spokesman said shortly after the incident.

"She is alive but undergoing urgent medical treatment on a nearby pier. We believe she fell from the bridge."

Also among the injured are three police officers, three French schoolchildren, aged 15 or 16, French officials said, as well as tourists from South Korea and Romania.

Witnesses have described the carnage on the bridge in the moments after the attack. People were lying across the road, some of them bleeding heavily, including one person under a bus, witnesses said.

Steve Voake, 55, said he was walking across the bridge towards South Bank when he saw at least two bodies lying on the road and one person in the water.

"I saw a trainer (a shoe) lying in the road and when I looked more closely I saw that there were a couple of bodies the other side of the road," he said.

"And when I looked over the side there was another body lying in the water with blood all around it."

Mobile phone footage also captured the frantic and chaotic moments on the bridge after the attack, including a phone call a witness made to emergency services to report the attack.

An unnamed man can be heard in footage telling the emergency operator: "There has been an accident. A car has just mowed down about three people on Westminster Bridge Road."

Operator: "Is the patient breathing?"

Caller: "There's about three of them, one is unconscious."

Bernadette Kerrigan told Sky News in London that she was on a tour bus when the attack occurred.

"As we were going across the bridge, we saw people lying on the floor, they were obviously injured. I saw about 10 people maybe. And then the emergency services started to arrive. Everyone was just running everywhere," she said.

Rick Longley told the Press Association said he was near Westminster tube station, just across from the Houses of Parliament and Westminster Bridge, when a "whole crowd" of people surged around the corner, just opposite Big Ben.

"A guy came past my right shoulder with a big knife and just started plunging it into the policeman. I have never seen anything like that. I just can't believe what I just saw," he said.

The policeman who died in the attack has been identified as Keith Palmer, a 48-year-old husband and father.