Shortly after that, police said there had been reports of stabbings at Borough Market. That's NPR's Frank Langfitt reporting from London.
The man with the knife stabbed a waitress, who was hiding behind a partition, in the neck and stabbed a man in the back before running out of the restaurant, the witness said.
He said a man was cut down behind him, with blood spraying onto Jag's shirt.
"I was just looking for the truth of the situation". And then there were nearly hundreds of people coming inside.
"Next thing we know, they're in our restaurant".
"She told me in French, "I don't know where those two other people are".
"She was bleeding heavily from the neck - it appeared that her throat had been cut. All Americans stand in solidarity with the people of the United Kingdom", she said.
"The guy with the knife was killing two people. Police came and shot straight away". At that point, I ran towards them. I've certainly never seen anything like it in my time here so far.
Gerard Vowls, 47, was watching the Champions League final at the Ship pub in Borough.
"London Bridge would have been very busy with pedestrians at this time of night".
He said the seriousness of the injuries is not yet known. "I've been walking around for an hour and a half crying my eyes out". The driver said something bad is happening here.
"I told people to turn around and run away".
It tweeted that people must "RUN - to a place of safety".
A Downing Street spokesman said: "The Prime Minister is in contact with officials and is being regularly updated on the incident at London Bridge".
British parliamentary elections are scheduled to be held Thursday.
Police in riot gear filled the streets and told pedestrians and reporters to run and leave the area as fast as possible. Armed police responded and shots were fired, police said.
We understand from Holly Jones that four pedestrians appear to be severely injured on London Bridge and that the van was going about 50 miles an hour, which is very odd. And at least one cab company tweeted an offer of free rides for people stranded in the area.
Vinny called LBC to say: "I was approaching London Bridge from Elephant and Castle and I saw police everywhere and people lying down on the floor".
Witnesses have reported seeing people hit by a vehicle on London Bridge.
Live video showed people streaming out of bars in the area with their hands raised above their heads.
LONDON is being rocked by a night of terror.
On Saturday evening, a vehicle plowed into more than 20 people on London Bridge.
A witness told the BBC she saw a speeding white van veering into pedestrians.
"He swerved right round me and then hit about five or six people".
"And then a couple of seconds later, about three police vans flew past". The assailant and four other people were killed, and 40 others were injured. "They all have paramedics assisting them at the moment".
London Bridge and nearby Borough Market in London are in lockdown after two separate attacks.
And in the popular food market in south London, witnesses said they saw a man with a large blade.
Here is a live Twitter stream regarding the incident.
The Metropolitan Police force says armed officers are responding at both scenes.
The van swerved into oncoming lanes before hitting a bus stop and coming to a stop, Roberts said. We're talking about central London. "Just bad. Whole city in lockdown", he tweeted. The patrons sheltered in the basement and police then arrived at the scene, the witness said.