One witness claimed on Twitter '15 to 20' people had been hit.
Another said a van had struck a crowd.
there are also unconfirmed reports of a knife attack following the crash, as well as gunshots being heard.
Martin Lucas said on Twitter: “Van drove into people on London Bridge, this is happening now. Really hope all are ok. We are in the middle of it.”
Police have advised people to keep away from the area.
Tubes are not stopping at London Bridge.
Video footage posted online shows a heavy police presence and people running from the scene.
A vehicle is said to have 'mowed into people' on London Bridge
A man can be heard shouting "everybody get out of here now."
Express.co.uk reporter Joey Millar is at London Bridge in the aftermath of the incident.
He said there was several armed police officers, a police heliopter and at least one person was being treated by paramedics.
Several passers by were in tears, he added.
One witness told Express.co.uk they saw a vehicle "mowing people down".
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They said they believed about five or six people were hit by the vehicle.
This is a developing story. More to follow…