Shocked witnesses said they saw bodies lying on the ground on Westminster Bridge near Parliament.
Scotland Yard said the attack in Westminster is being treated "as a terrorist incident until we know otherwise".
One witness said she saw an Asian man carrying an eight-inch knife heading towards the building.
Jayne Wilkinson said: "We were taking photos of Big Ben and we saw all the people running towards us, and then there was an Asian guy in about his 40s carrying a knife about seven or eight inches long.
There was an Asian guy in about his 40s carrying a knife about seven or eight inches long
Witness Jayne Wilkinson
"And then there were three shots fired, and then we crossed the road and looked over. The man was on the floor with blood.
"He had a lightweight jacket on, dark trousers and a shirt.
"He was running through those gates, towards Parliament, and the police were chasing him."
Her partner David Turner added: "There was a stampede of people running out.
London Terror Attack: LIVE IMAGES Wed, March 22, 2017
Two people shot outside Parliament as car mows down 10 people in Westminster
Getty Images 1 of 22
A member of the public is treated by emergency services near Westminster Bridge and the Houses of Parliament
Get Quotes on Home Insurance
"You saw the people and you thought 'what the hell is going on'."
After the incident, Radoslaw Sikorski posted a video to Twitter purporting to show people lying injured in the road on Westminster Bridge.
Mr Sikorski, a senior fellow at Harvard's Centre for European Studies, wrote: "A car on Westminster Bridge has just mowed down at least five people."
At least four people were seen lying on the ground, some bleeding heavily and apparently unconscious, on Westminster Bridge near Britain's parliament on Wednesday, Reuters photographs showed.
One of the photographs showed a body lying under the wheels of a London bus.
An assailant was shot outside parliament by armed police, the leader of the House of Commons said on Wednesday after loud bangs were heard and a Reuters photographer saw at least a dozen injured people on the nearby bridge.
Witness Quentin Letts said he saw a man in black attack a police officer outside Parliament before being shot two or three times as he tried to storm into the House of Commons.
"I saw a thick-set man in black clothes come through the gates into New Palace Yard, just below Big Ben," he told the BBC.
"He had something in his hand, it looked like a stick of some sort, and he was challenged by a couple of policemen in yellow jackets.
"And one of the yellow-jacketed policemen fell down and we could see the man in black moving his arm in a way that suggested he was stabbing or striking the yellow-jacketed policeman."
Parliament shooting: Witness reveals knifeman ran towards Parliament
Scotland Yard are treating the incident as a terror attack
He other officer ran to get help and the man in black ran about 15 yards towards the entrance.
Mr Letts said: "As this attacker was running towards the entrance two plain-clothed guys with guns shouted at him what sounded like a warning, he ignored it and they shot two or three times and he fell."
Kevin Schofield, the editor of PoliticsHome.com heard "a very loud bang" from the press gallery inside the Houses of Parliament followed by lots of shouting and men running around.
He initially thought it was a car crash but then he looked outside the window to a heavily-guarded area outside which is out of bounds to the public.
He told Sky News: "Someone rushed through, attacked a policeman, a policeman went down, another policeman came and he was rescued.
"The man who had assaulted him got up and he appeared to be carrying either a knife or a gun. Then we heard gunfire, lots of gunfire, maybe five or six rounds.
Shocked witnesses said they saw bodies lying on the ground on Westminster Bridge near Parliament
"All I remember seeing is the man approaching the police officer probably with a knife and then there was gunfire.
"He was walking towards a second policeman with his arm outstretched, with what looked like a knife in his hand, having already assaulted another policeman.
"It was at that moment that you realised that something serious was happening – a man had broken in to Parliament and had a weapon."
More to follow…