At least 48 people were also injured in the attack that took place last night at around 10 pm, the third to hit Britain in less than three months and just days before the general election on June 8.
Three attackers drove a white van into crowds on busy London Bridge and then fled the van wielding large knives and attacked people indiscriminately at bars and restaurants in nearby Borough Market shouting "This is for Allah", police and witnesses said.
The attack unfolded quickly as armed police rushed to the scene and within eight minutes shot dead the three male attackers who were wearing what looked like explosives which later turned out to be fake.
"The suspects were wearing what looked like explosive vests but these were later established to be hoaxes," said Mark Rowley, Met Police Assistant Commissioner and the UK's anti-terrorism lead.
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"We are treating this as a terrorist incident and a full investigation is already underway, led by the Met's Counter Terrorism Command," he said, urging people with information and images to contact the police.
British counter-terrorism police said they had arrested 12 people in Barking, in east London, in connection with the van and knife attack.
The arrests followed a raid by police at a flat owned by one of the three attackers.
Police said that "a number of addresses" in Barking were still being searched.
National campaigning for the June 8 general election was suspended for the day in respect to the victims, but Prime Minister Theresa May insisted that the elections would go ahead as planned.
She said "it is time to say enough is enough" and called for tougher measures to contain Islamic extremism in Britain.
She said the recent terror attacks in Britain, while not directly linked, "are bound together by the single evil ideology of Islamist extremism."
"It is an ideology that is a perversion of Islam and a perversion of the truth. Defeating this ideology is one of the great challenges of our time."
The prime minister said attacks are now inspired "by copying one another and often using the crudest of means of attack".
"We cannot and must not pretend that things can continue as they are," she said.
She revealed that the UK's security and intelligence services have disrupted "five credible plots" since the Parliament attack in London in March.
The British Prime Minister announced that she plans to review the UK's counter-terror legislation.
"There is far too much tolerance for extremism in our country," she said.
The area that came under attack last night is one of the London's most popular hangout areas for a weekend with bars, restaurants and clubs.
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.
"We are reviewing and planning to strengthen our policing stance across London over the forthcoming days, and there will be additional police and officers deployed across the capital," Rowley said, calling on the public to remain vigilant.
London Mayor Sadiq Khan called it "a deliberate and cowardly attack on innocent Londoners".
"We will never let the terrorists win or cower our citizens," he said.
The Indian High Commission in London has set up a Public Response Unit for any Indians caught up in the attack.
"Any Indians injured/affected during the London Bridge 'major incident' and at Borough Market may reach off-office hours Public Response Unit. We shall endeavour to extend all possible assistance to all affected and to their families and friends in this difficult hour," an Indian High Commission statement said.
Prime Minister Narendra Modi also condemned the attacks in London, terming them as "shocking".
"Attacks in London are shocking & anguishing. We condemn them. My thoughts are with families of the deceased & prayers with the injured," the Prime Minister said in a tweet.
The latest terror attack, just four days before the general election on June 8, comes less than two weeks after a suicide bomber, Salman Abedi, targeted a Manchester concert on May 22, killing 22 people.
Britain's terror threat was later lowered back to "severe", which meant that an attack was highly likely.
Jeremy Corbyn, the Opposition Labour leader, tweeted, "Brutal and shocking incidents reported in London. My thoughts are with the victims and their families. Thank you to the emergency services."
Tim Farron, the Liberal Democrat leader, said: "Tonight's horrific incidents in London remind us how much we owe our emergency services. My thoughts and prayers with everyone affected."