In response to the wave of attacks, she listed four key points that needed to change in order to tackle the threat of extremism.
"A van came from London Bridge itself, went between the traffic light system and rammed it towards the steps", a taxi driver told the BBC. It knocked loads of people down. My thoughts with the victims and families - and huge thanks to emergency services. "Our thoughts are with those who are caught up in these terrible events".
President Donald Trump offered the help of the USA and said: "Whatever the United States can do to help out in London and the UK, we will be there - WE ARE WITH YOU".
"Canadians stand united in sending our love and support to our friends in London". "But the whole of our country needs to come together to take on this extremism, and we need to live our lives not in a series of separated, segregated communities, but as one truly United Kingdom".
Of the casualties, he said: "Three of them, yes (were conscious), and one guy was not talking at all, was just, like, down".
In another tweet, he advised: "We need to be smart, vigilant and tough". "We need to work with allied democratic governments to reach worldwide agreements that regulate cyberspace". "We need to do everything we can at home to reduce the risks of extremism online".
After the vehicle mowed people down on the bridge, witnesses reported seeing at least one man carrying a large knife.
"Police say the incidents occurred on the bridge and at Borough Market a short distance away".
Many night revelers and tourists have grown "increasingly frustrated" and are "feeling not very safe", unable to get back to their hotels because they happened to be in the sealed area.More news: Real Madrid Wins Champions League Battle With a 4-1 Victory
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London Mayor Sadiq Khan - elected previous year and the first Muslim to head a major Western capital - had earlier said Britons should not be alarmed to see a higher police presence on the streets of London following the incident.
Police said they were called just after 10 p.m. local time to reports of a vehicle hitting pedestrians on the bridge, which crosses the River Thames in central London.
"Within my line of sight, there were five or six people on the ground that were not moving", he said. Reuters television pictures showed dozens of emergency vehicles in the area around London Bridge.
Roberts said he heard what sounded like gunshots about 10 minutes later.
A van has mounted the pavement on London Bridge before a stabbing attack, according to witnesses.
'We cannot and must not pretend things can continue as they are, ' May said in a televised statement in front of her Downing Street office.
The area has been cordoned off for investigations, led by the Met Police s Counter Terrorism Command, working with British Transport Police, City of London Police, the London Ambulance Service and the London Fire Brigade.
Police activity spread throughout the Borough Market area. "They were running up and going "This is for Allah", a man called Gerard told the BBC, adding that he had seen the assailants stabbing a girl and had tried to confront them.
Britain is on high alert only 12 days after a suicide bomber killed 22 people at the concert in Manchester, northwest England, and ahead of the June 8 vote, in which security is a major theme.