British police rushed to an incident on London Bridge on Saturday after witnesses said a van ploughed into pedestrians.

Armed police rushed to the scene and within eight minutes of receiving the first emergency call had shot dead the three male attackers in the Borough Market area near the bridge.

The attacks came just five days ahead of a parliamentary election on Thursday. The ruling Conservative Party suspended national campaigning on Sunday, a spokesman for Prime Minister Theresa May said.

'Following updates from police and security officials, I can confirm that the terrible incident in London is being treated as a potential act of terrorism,' May said in a statement as events unfolded.

London Mayor Sadiq Khan said some of those who had been injured were in a critical condition.

Khan said the official threat level in Britain remained at severe, meaning an attack is highly likely. It had been raised to critical after the Manchester attack, then lowered again days later.

The mayor also said he did not think Thursday's election should be postponed because of events in London.

'One of the things that we can do is show that we aren't going to be cowed, is by voting on Thursday and making sure that we understand the importance of our democracy, our civil liberties and our human rights,' Khan said.