A van reportedly swerved off the road on London Bridge and in the popular food market in south London, witnesses said they saw a man with a large blade.
Scotland Yard have said they are responding to three incidents, in London Bridge, Borough Market and Vauxhall.
Husband and wife Ben and Natalie told BBC Radio 5 Live they were outside Borough Market, coming up the entrance of the underground when they saw the incident.
Ben said: “We saw people running away and then I saw a man in red with a large blade, at a guess 10 inches long, stabbing a man, about three times.
“It looked like the man had been trying to intervene, but there wasn’t much he could do. He was being stabbed quite coldly and he slumped to the ground.”
Ben said the man walked away boldly with another person, and went towards the Southwark Tavern. He said they saw a metal chair being thrown towards the man.
“Then we heard three gunshots, definitely gunshots, and we ran.”
London Bridge is closed both ways Tfl said, warning the public to avoid the area.
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. I saw a young girl stabbed in the chest.
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.”
The Prime Minister will chair a meeting of the Government’s Cobra emergency committee on Sunday, No 10 said.
Facebook has activated its safety check for people in London to let loved ones know they are OK.