Eyewitnesses say at least 12 people were injured on the bridge, while a Ferry appears to have crashed into it and another vehicle has crashed into a fence outside the Parliament.
There are now unconfirmed reports more than one person has died.
At least four people were lying on the ground on the bridge, some bleeding heavily and apparently unconscious.
One photograph showed a body lying under the wheels of a London bus.
The vehicle has been described as a four-wheel drive – and the driver was described as a middle-aged Asian man who carried a large knife.
Horrifying images have begun to emerge of Westminster Bridge
Pictures are emerging on social media
David Lidington, the leader of the House of Commons, told parliament a police officer was reportedly stabbed inside Westminster.
Meanwhile, witnesses have said they heard sounds like gunfire near Parliament.
MPs are being kept inside.
Police on scene have said at least one of the three incidents is a firearms incident.
Armed officers reportedly opened fire and shot a person outside the Houses of Parliament.
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Police and paramedics are on scene in Westminster
A number of shots were fired at around 2.35pm moments after a loud bang was heard inside the Palace estate.
According to eyewitnesses there was three bodies were visible on the floor.
The House of Commons has been suspended by Deputy Speaker Lindsay Hoyle.
Pedestrians stop to help injured person on Westminster Bridge
Alan Parry from Sky Sports News said: "I was just outside Westminster tube station when I heard an almighty crash and a vehicle that looked like a 4×4 had crashed into railings. There was smoke coming from underneath the bonnet. I saw a pedestrian or a cyclist who had clearly been hit.
“The driver sprinted away from the scene. That was followed by four what sounded very much like gunshots. Then all of a sudden all hell was let loose and police descended everywhere. The whole area was locked down."
People have been seen fleeing the area.
The incident follows Prime Minister's Questions (PMQs).
Westminster Bridge has been closed to pedestrians
And then there were three shots fired, and then we crossed the road and looked over. The man was on the floor with blood
Jayne Wilkinson told Sky News: "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.
"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."
A car was crashed outside parliament – one person can be seen on the floor
Walking thru Commons cloisters to vote, heard 4 gunshots. Police had MPs hit ground & crawl to cover.
— Grant Shapps (@grantshapps) March 22, 2017
Gunfire at Westminster
A Met Police spokesman, said: "Police were called at 14.40 to a reports of an incident on Westminster Bridge.
“It’s being treated as a fire arms incident. Officers are on the scene and dealing.”
British Prime Minister Theresa May is safe.
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Two people shot outside Parliament as car mows down 10 people in Westminster
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A member of the public is treated by emergency services near Westminster Bridge and the Houses of Parliament
There have been three incidents, according to reports, at Westminster Palace and on the bridge
Westminster Station has been closed and the London Eye is out of operation.