UPDATE: Police are now referring to the car attack and Borough Market stabbings as a "terrorist incident."
From the BBC, also reports of stabbings and shots fired:
More than one person has died after an incident involving a vehicle and stabbings in the London Bridge area of the capital, police have said.
Armed police responded to reports of a van hitting pedestrians on the bridge in central London.
The Met Police said officers were also at Borough Market nearby where they were responding to reports of stabbings.
The force said they were also attending a reported incident in Vauxhall.
In another apparently related incident:
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.
Witnesses reported hearing gunshots at the bridge around 10:30 p.m.
“I heard many gunshots and I heard people running away,” said Joe Dillon, 23, who was near London Bridge when the incident occurred. “Police officers were shouting: ‘Get out of here, you need to go!’ I heard at least eight rounds of gunshots, but I’m not sure who was shooting. When I arrived a second after I had heard the screams and the shots, I saw five or six officers running toward the van.”
The incident caused chaos in the heart of London in an area normally bustling on a Saturday night. Pedestrians near the bridge said they were ordered by police to run. Diners at nearby restaurants were told to shelter in place. Video footage showed people fleeing.
Saturday’s incident comes less than two weeks after 22 people were killed in a bomb blast following a Manchester concert. And it comes less than three months after a driver killed four pedestrians on another Thames crossing, Westminster Bridge. The assailant then stabbed to death a London police officer at the gates of Parliament.