May confirmed that 48 people were being treated in hospitals across London any many had life-threatening injuries. It was not entirely clear if the police operation was over.
Prime Minister Theresa May was to chair a meeting of Britain's Cobra emergency committee on Sunday in response to the "dreadful events".
Assailants drove a van into pedestrians at high speed on London Bridge on Saturday night before stabbing revellers on nearby streets, in what police described as a suspected terrorist attack.
In one of the incidents, a van speeding across the London Bridge suddenly veered off the road and hit several pedestrians on the pavement.
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The Metropolitan Police advised people caught up in the incidents to "RUN - to a place of safety".
London Bridge Tube station was closed and London Bridge was closed in both directions.
The Scottish National Party and the Liberal Democrats also announced that they were temporarily suspending their campaigns, but Paul Nuttall, the leader of the anti-immigration UKIP, refused to do so "because this is precisely what the extremists would want us to do".
- Metropolitan Police (@metpoliceuk) June 3, 2017As well as #LondonBridge officers have also responsed to an incident in #BoroughMarket.
He was then shot dead by police at the scene.
A witness told CNN two men entered a restaurant at Borough Market, just south of London Bridge, and stabbed two people inside. Reuters television pictures showed dozens of emergency vehicles in the area around London Bridge. They did not say if officers fired the shots.
As they responded to the two incidents, police were then called to a third potential attack - reports of an "incident" in nearby Vauxhall, a residential area, which occurred just before 1 a.m. (8p ET).
"They are bound together by the single evil ideology of Islamist extremism that preaches hatred, sows division, and promotes sectarianism", she said.
"Is a new abominable, cowardly attack on our free societies", the presidency said. He urged people to remain calm and vigilant. "We condemn them. My thoughts are with families of the deceased & prayers with the injured", the Prime Minister said in a tweet.
"Whatever the United States can do to help out in London and the U".
"Did you notice we are not having a gun debate right now? GOD BLESS!" Trump tweeted.
Authorities declared the incident a terrorist attack. On March 22, 52-year-old Briton Khalid Masood drove a vehicle into pedestrians on Westminster Bridge, injuring dozens of people.
Leader of the Opposition, Jeremy Corbyn, Liberal Democrat leader Tim Farron and Mayor of London Sadiq Khan all took to Twitter to express solidarity with those affected and to thank the emergency services.
England has been on edge since May 22, when a suicide bomber killed 22 people at an Ariana Grande concert at the Manchester Arena.
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