Downing Street said Prime Minister Theresa May, who has been campaigning in the General Election, was returning to Number 10 to receive further briefings from security officials.
In a statement, the 60-year-old Conservative leader 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.
“This is a fast moving investigation. I want to express my huge gratitude to the police and emergency services who are on the scene. Our thoughts are with those who are caught up in these dreadful events.”
London mayor Sadiq Khan has described the incident as a deliberate and cowardly attack.
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London Bridge terror attack: Jeremy Corbyn responds to ‘brutal and shocking incident’
We don't yet know the full details, but this was a deliberate and cowardly attack on innocent Londoners and visitors
Mr Khan said: “We don't yet know the full details, but this was a deliberate and cowardly attack on innocent Londoners and visitors," Khan said. "I condemn it in the strongest possible terms. There is no justification whatsoever for such barbaric acts.”
Mr Khan also confirmed he would partake in a security meeting with the Prime Minister later today.
Labour leader Jeremy Corbyn took to Twitter to praise the police after rushing to the scene after a van on London Bridge ploughed into pedestrians, and reports of stabbings and gunfire.
One police officer at the scene described the incident as a "terror attack" to Express.co.uk.
London Bridge terror attack: Jeremy Corbyn tweets about the incident
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London Bridge terror attack: Police clear the area
Mr Corbyn tweeted: “Brutal and shocking incidents reported in London. My thoughts are with the victims and their families. Thank you to the emergency services.”
Liberal Democrats leader Tim Farron, 47, posted: “Tonight's horrific incidents in London remind us how much we owe our emergency services. My thoughts and prayers with everyone affected.”
UKIP leader Paul Nuttall, 40, wrote: “Worrying scenes at London Bridge tonight. My thoughts are with those caught up in it. I hope everyone is okay.”
Nigel Farage revealed that he was close to London Bridge when tonight’s incident took place.
The 53-year-old tweeted: “Was very close to London Bridge when incident happened. Sounds like another disaster.”
The White House has announced that President Donald Trump has been briefed by his national security team.
Home Secretary Amber Rudd called last night’s events “a horrific attack in the heart of our capital city” and said she was “extremely proud of our emergency services” for their response to the attacks.