Prime Minister Theresa May is now on her way to Downing Street to receive further briefings from security officials.

The US state department says it is closely monitoring London's incidents, Reuters reports. The department advises US nationals in the UK to heed local authorities.

Foreign correspondent for MSNBC tweets...

A security guard who oversees a number of pubs in the area has told the BBC he saw four people stabbed by three attackers.

The man, who was deeply shocked and asked not to be named, said he was at the Market Porter pub when a colleague at another bar said there was a stabbing at the Borough Bistro pub nearby.

He said he went towards this pub and saw that "everybody started running" and there was screaming.

The eyewitness added that he saw three attackers, one of whom had a long knife and stabbing people, including a girl in her early 20s.

Bank and Vauxhall stations have now reopened, Transport for London confirms.

Metropolitan Police tweets...

The social media site has activated its safety check to let people know they are safe.

BBC Radio 5 live

Natalie and Ben were coming up to the entrance of the underground on Borough High Street when they saw lots of people running.

The married couple witnessed someone being stabbed.

Ben said: "I saw a man in red with quite a large blade, I don't know the measurement I guess maybe 10 inches. He was stabbing a man...he stabbed him about three times fairly calmly.

"It looked the man had maybe been trying to intervene but there wasn't much that he could do he was being stabbed quite coldly and he slumped to the ground.

The attacker and another man walked off quite "boldly".

"A table was thrown, a bottle was thrown at the individual with the knife and then we heard three gunshots and we ran," he added.

Here's a recap of what we know so far:

• Police confirm there is more than one fatality
• Reports suggest there is more than one incident
• First, a white van hits pedestrians at London Bridge at about 22:15
• A short time later there are reports of men carrying knives at Borough Market. Armed officers responded and shots were fired
• A third incident is taking place at Vauxhall, Scotland Yard say

Metropolitan Police tweets its latest advice for anyone at the three incidents in central London.

Police at the cordon at the south side of London Bridge says there is more than one fatality

The BBC's Nick Quraishi at the scene says he is now able to corroborate earlier reports of gunshots being fired.

Reports suggest it may have been more than one incident:

- A van hitting people at London Bridge and three people then jumping out of the vehicle and attacking members of the public;

- A separate incident at Borough Market

- Police have now said they are responding to a third incident in Vauxhall

It is understood that police are looking for three suspects who may be armed.

BBC security correspondent tweets...

Police are responding to an incident in Vauxhall in south London, Scotland Yard said.

An eyewitness told LBC radio what he saw tonight.

The taxi driver said: "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."

Frank Gardner
BBC Security Correspondent

Whitehall officials say the police are leading on this incident, not intelligence agencies.

It appears to have taken the authorities by surprise, i.e. there was no intelligence warning or surveillance indicating this was about to happen.

Some people are providing offers of somewhere to stay and a home cooked meal.

The White House press secretary has confirmed the president is being kept informed about the incident.