A van is believed to have mounted the kerb on London Bridge and ploughed into pedestrians at about 10.10pm this evening.
There have also been reports of stabbings and sounds of gunfire in Borough Market.
Police have advised people to keep away from the area. The Shard and the News Building are on lockdown.
The Met tweeted an image instructing the public to "Run, Hide, Tell".
Armed police opened fire on one man at Borough Market
Police have confirmed they are investigating an act of terrorism
Will Heaven, a journalist for the Spectator who was at the scene shortly afterwards, wrote on Twitter that he had seen casualties – one on the pavement and one on the edge of the road.
He told Sky News: "It was about 10.15pm I was in the back of an Uber cab driving over London Bridge…there was somebody down on the pavement with a small crowd around them clearly very concerned about their welfare.
London Bridge terror: Scenes as armed police respond Sun, June 4, 2017
At least two people have died after being after reportedly being struck by a van on London Bridge on Saturday night.
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Armed police responding to the incident at London Bridge
"The penny dropped that something quite serious was happening.
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"Suddenly the traffic came to standstill. The driver said something bad is happening here.
"We could hear sirens coming and then suddenly ahead of us we noticed another casualty in the road."
The London Bridge area has been evacuated following the attack
Two people have so far been confirmed dead
Hundreds of pedestrians were escorted from London Bridge with their hands on their heads.
A third incident in Vauxhall has been confirmed as a stabbing but not terror related.
Reported explosions around the London Bridge area were confirmed as controlled and monitored by the police.
There are reports of attackers carrying large knives stabbing people at random
Much of Central London remains on lockdown
Prime Minister Theresa May issued a statement confirming the incident as a terror attack.
She will chair an emergency COBRA meeting tomorrow morning.