British police rushed to an incident on London Bridge on Saturday after witnesses said a van ploughed into pedestrians and one woman told Reuters she saw people who may have had their throats cut.

British Transport Police said casualties were reported after an incident that may have involved a van and a knife attack, the BBC said, while the London Ambulance Service said it was sending multiple resources to the incident.

Police said armed officers were also responding to an incident in the nearby Borough Market area of the city.

One witness told Reuters that she saw what appeared to be three people with knife wounds and possibly their throats cut at London Bridge. Reuters was unable to immediately verify her account.

Another witness told the BBC she saw a speeding white van veering into pedestrians. That witness said the van hit five to six people. Reuters television pictures showed dozens of emergency vehicles in the area around London Bridge.

Several witnesses also reported hearing gunshots.

"We were in an Uber (taxi) going towards London Bridge and suddenly we saw people running. The Uber stopped, we asked people what was going on – people said there was shooting," said Yoann Belmere, 40, a French banker living in London.

"Now the area is completely closed with police cars going one way and ambulances going the other," he told Reuters.

London's transport authority said London Bridge rail station had been closed at the request of the police.

The incident comes days ahead of a June 8 election, with polls suggesting the lead of Prime Minister Theresa May's Conservative Party has dropped sharply.

It also comes less than two weeks after a suicide bomber killed 22 people at a pop concert by U.S. singer Ariana Grande in Manchester in northern England.

The Manchester bombing on May 22 was the deadliest attack in Britain since July 2005, when four British Muslim suicide bombers killed 52 people in coordinated attacks on London's transport network.