There are reports of “multiple” casualties following a major incident on London Bridge, British Transport Police said.
Nick Brandon of the BTP’s force control room said he had received reports of an incident possibly involving a knife and a vehicle.
The seriousness of the injuries is not yet known, he said.
He said trains were not stopping at London Bridge and Borough Market.
Police are also responding to an incident at Borough Market, Scotland Yard said.
Armed police were at both scenes, the force added.
A Downing Street spokesman said: “The Prime Minister is in contact with officials and is being regularly updated on the incident at London Bridge.”
London Bridge is closed both ways Transport for London (TfL) said, warning the public to avoid the area.
Trains are currently not stopping at London Bridge or Borough stations.
Scotland Yard said officers were at the scene and it would update with further information.
London Ambulance said multiple resources were attending the area.
Holly Jones, a BBC reporter at the bridge when the incident happened, said a van had swerved off the road into a crowd of pedestrians.
“A white van driver came speeding – probably about 50mph – veered of the road into the crowds of people who were walking along the pavement,” she told BBC News.
“He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind.
I’d say there are about four severely injured people. They all have paramedics assisting them at the moment.”
Ms Jones said police were on the scene within two minutes, quickly followed by ambulances.
Police boats were searching the river – apparently looking for people who may have been thrown off the bridge.
She said that among the injured was a French woman who told her she did not know where the two people who had been with her were.
“She told me in French, ‘I don’t know where those two other people are’. So the police checking the Thames,” Ms Jones said.
“They were right near the edge of the bridge. It looks potentially they could have been thrown over.”
Police are treating injured people and carrying them away at the end Thrale Street. Members of the public were told by police to “run as fast as they could” westbound.
Nick Archer, who was in the London Bridge area, told Sky News: “We came out (of a bar) on to the road and looked and looked to my left and there as a guy, I thought he was just drinking but he was lying on the floor.
“And then a couple of seconds later, about three police vans flew past.
“He looked in a bad way.”
A taxi driver called Chris told LBC said he saw men armed with foot-long knives after a van drove on to the pavement.
He told the station: “I didn’t see the van mount the kerb, but I saw everything else.
“A van came from London Bridge itself, went between the traffic light system and rammed it towards the steps. It knocked loads of people down.
“Then three men got out with long blades, 12 inches long and went randomly along Borough High Street stabbing people at random.”
One witness reported having seen a van crashed into a lamppost after the bridge by the Barrowboy and Banker pub.
She added: “Just trying to get away at the moment. There are no trains leaving so we’re just panicking a little.”
Tony Murphy, who lives near the area, told Sky News he heard the sound of gunfire.
He said: “I thought at first it was fireworks then I recognised it was significant gunfire and that was the first instance.
“After that (came) the whole shooting match of ambulances and police.
“There was rapid fire because that’s why I thought it was fireworks.”
Will Orton, 25, told the Press Association: “We were in the Sheaf pub. Basically lots of people came running inside, we didn’t really know what was going on.
“We thought maybe there was a fight or something outside. And then there were almost hundreds of people coming inside.
“The bouncers did a really good job, they shut the doors and locked everyone in.
“There was panic – it seemed like it was literally outside the door.
“People were coming inside and saying they had witnessed people being stabbed.
“They had seen and witnessed people being stabbed.
“It seemed like it was happening immediately outside the entrance.”