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 Centre for European Studies, said he saw at least five people lying on the ground after being "mown down" by a car.
"I heard what I thought what I thought was just a collision and then I looked through the window of the taxi and someone down, obviously in great distress," he told the BBC.
"Then I saw a second person down, and I started filming, then I saw three more people down, one of them bleeding profusely."
A line of red buses and several ambulances could be seen on Westminster Bridge.
Alex Wafer, 47, who was cycling nearby and saw the aftermath, said: "At the end of the embankment it appears as though there is an ambulance.
"It looks as if they are treating somebody.
"And just below, it looks like there may be another paramedic treating someone else."
A car on Westminster Bridge has just mowed down at least 5 people. pic.twitter.com/tdCR9I0NgJ— Radosław Sikorski MEP 🇵🇱🇪🇺 (@sikorskiradek) March 22, 2017
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.
"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."
Alan Parry, of Sky Sports News, was at Westminster for a meeting when he heard "an almighty crash" when he was just outside the underground station .
He could see what he thought was a 4x4 vehicle on the other side of the road which had crashed into some railings.
He told Sky News: "There was smoke coming this vehicle. I walked on a few paces further and saw what I assumed to be either a pedestrian or a cyclist who had clearly been hit and wasn't moving, although he did then gently move.
"The guy who I assumed was the driver of this 4x4 got out of the car and suddenly sprinted away from the scene - that was followed by four of what sounded much like gunshots.
"All of a sudden all hell was let loose. Police descended everywhere and the whole area was locked down."
Steve Voake, 55, was walking across the Westminster Bridge towards the South Bank when he saw the aftermath.
He said he saw at least two bodies lying on the road and one in the water.
"I saw a trainer 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 told the Press Association.
"And when I looked over the side there was another body lying in the water with blood all around it."
Witness Richard Tice said he "counted between eight and 10 prostrate figures on the ground" after he came out of Westminster underground station and moved on to Westminster Bridge.
He told Sky News: "My understanding from someone who was standing next to me was that a car had driven along the whole pavement knocking people over and that is why there were many injuries. The people lying on the ground were starting to be attended to by a paramedic."
Matt Haikin, from London, 44, said he was in shock after seeing the aftermath of the crash on the bridge.
He said: "I just saw a car that had clearly driven off the road into the fence outside Parliament.
"As I went past I noticed there was a body next to it and quite a lot of blood and people standing around.
"Fairly shortly after I heard some shots, at which point it was clear it wasn't just an accident, something else was going on."
He then moved to look through the Palace of Westminster gates and saw "a lot of people, people in uniform, I think I saw a couple of bodies on the ground, I couldn't tell you if they'd been asked to lie down or if they were injured".