The Metropolitan police tweeted that officers are on the scene, which is just minutes from the bridge in the heart of the City, where they were reportedly responding to a "stabbing".
There has been at least one confirmed fatality, according to police.
A taxi driver called Chris told LBC he saw men armed with foot-long knives after a van drove on to the pavement.
He told the station: "I didn't see the van mount the kerb, but I saw everything else.
Armed police are reportedly responding to a second incident in Central London
"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. I saw a young girl stabbed in the chest.
Armed police are on the scene
Officers are now responding to a third incident in Vauxhall, less than a mile from London Bridge.
The tweet read: “As well as #LondonBridge officers have also responsed to an incident in #BoroughMarket.
“We have armed police at the scenes.”
Dramatic footage from the area, which is popular with diners and tourists, shows police running into Katzenjammers bar, instructing panicked revellers to “get down”.
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