Seven innocent people have died following the London terror attack, Metropolitan Police commissioner Cressida Dick has just announced.
The death toll had stood at 6. There are still 48 people injured.
Commissioner Dick praised the "remarkable" bravery of the emergency services personnel and sought to reassure Londoners about their safety.
"Many, many people risked their own safety to help others and to treat those seriously injured, and, indeed, to confront the suspects involved. It's clear to me that the courage of those people during and following the attack was extraordinary and I pay tribute to all of them who came to the aid of those in need during this dreadful attack," Commissioner Dick said.
"I can tell you we will be doing absolutely everything in our power to try to stop such an horrendous attack as this."
EARLIER: Six people were killed and more than 30 injured when a van driving at high speed mowed down pedestrians on London Bridge, before the occupants got out and began stabbing patrons at nearby bars and restaurants, in what police have declared as a terrorist attack.
Police said the three attackers, who were wearing what appeared to be explosive vests, were then shot dead in a confrontation with police outside the popular Borough Market, which was packed with people on Saturday night.
Metropolitan Police Assistant Commissioner Mark Rowley said police officers shot dead the suspects within eight minutes of receiving the first emergency call. The vests the men were wearing were later determined to be fake, he said.
"Sadly, six people have died in addition to the three attackers shot by police," Commissioner Rowley, Britain's top anti-terrorism officer, said.
The attack began just after 10pm on Saturday, local time, when a white van travelling at up to 80km/h ploughed into pedestrians on London Bridge.
Related coverage:London Bridge closed as van ploughs into pedestrians
A number of people were run over, while witnesses said some people jumped into the River Thames to escape.
Three men then got out of the vehicle and ran towards the nearby Borough Market. They were armed with long knives and started stabbing people as they ran, witnesses said.
An on-duty British Transport Police officer received "serious injuries" including head, face and leg wounds, as he responded to calls for help from the public, Commissioner Rowley said.
The attacks occurred on a Saturday night in an area where hundreds of people were enjoying themselves in bars and restaurants. Patrons threw chairs, bottles and glasses at the attackers as they used long knives to slash their way through crowds, witnesses said.
An image broadcast by the BBC showed a man, apparently one of the assailants, lying prone with what appeared to be metal canisters strapped to his body.
About three hours after the initial attacks, three loud explosions were heard near Borough Market.
British Prime Minister Theresa May said the incidents were being treated as a potential act of terrorism.
"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," May said, just over four days before voting is due to begin in a June 8 national election.
"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."
Just before 12.30am, local time, Metropolitan Police declared the two attacks to be terrorist incidents.
London Ambulance said it had taken 30 patients to five hospitals across London.
The BBC said one of its journalists, Holly Jones, was on London Bridge at the time and said the van was "probably travelling at about 50 miles an hour (80km/h)". Jones estimated about five people were injured after the van mounted the gutter.
"He swerved right round me and then hit about five or six people. He hit about two people in front of me and then three behind," Ms Jones told the BBC News Channel.
She said the van, which was travelling from the direction of central London, headed towards the south side of the river.
Witnesses also reported hearing gunshots at the bridge around 10.30pm, local time.
"I heard many gunshots and I heard people running away," said Joe Dillon, 23, who was near London Bridge when the incident occurred.
"Police officers were shouting: 'Get out of here, you need to go!' I heard at least eight rounds of gunshots, but I'm not sure who was shooting. When I arrived a second after I had heard the screams and the shots, I saw five or six officers running toward the van."
One witness told Reuters that she saw what appeared to be three people with knife wounds and possibly their throats cut. Police have not confirmed this report.
The managing editor of the Spectator magazine, Will Heaven, tweeted that he was on London Bridge and saw "injured pedestrians, first responders, armed police, people running north".
What I saw: injured pedestrians, first responders, armed police, people running north. What I heard of: stabbings, injured. #LondonBridge— Will Heaven (@WillHeaven) June 3, 2017
Police later confirmed a second incident at Borough Market, which is near the bridge on the south side of the river.
One cab driver told The Telegraph in London that three men ran towards the market stabbing people - including a young girl - as they ran.
Police entered bars and restaurants in the Southwark area around 11pm and told customers to get down on the floor. People outdoors were told by yelling officers to run from the area amid chaotic scenes.
Steph, 22, and her friend Cate, 24, were heading to London Bridge station to catch the train to Tonbridge Wells in Kent, but as they were walking through Borough Market they were rushed into a pub and held in the basement for an hour.
"People around us had heard gunshots, we were in the basement for an hour," Steph said.
They said about 100 people were in the pub and were told to turn off their phones.
The pair told Fairfax Media that police had wanted to use boats to ferry the passengers to the other side of the Thames. Women and children were sent out first.
Cate had a stern message for the terrorists: "F*** them".
"You know it's [attacks are] going to happen with the current climate, and you hope that you're strong enough to get through it," she said.
"We were all strong together."
British police are believed to be searching for three suspects who may be armed, the BBC reported.
It was initially feared that a separate stabbing in the Vauxhall area about the same time was part of the attack, but the Metropolitan Police later said it was an unrelated incident.
No Australians injured
Foreign Minister Julie Bishop said she had been in contact with UK High Commissioner Alexander Downer, and there were no initial reports of Australian casualties.
"We stand ready to support the British government as it responds to these attacks and our thoughts are with those injured and their families," she said.
Prime Minister Malcolm Turnbull has declared Australia's "absolute solidarity" with Britain after the attacks.
"Our prayers and resolute solidarity are today as always with the people of Britain in the face of the shocking terrorist attacks in London," Mr Turnbull tweeted.
The incident comes less than two weeks after 22 people were killed in a bomb blast following a Manchester concert. And it comes three months after a driver killed four pedestrians on another Thames crossing, Westminster Bridge. That assailant then stabbed to death a London police officer at the gates of Parliament.
The mayor of London, Sadiq Khan, called the incidents a "deliberate and cowardly attack on innocent Londoners".
Labor senator Sam Dastyari said on social media he was having dinner near the London Bridge and was evacuated past the scene by police after they placed the restaurant in lockdown.
Fairfax Media correspondent Latika Bourke said she saw dozens of people being evacuated from the area.