Three men then got out of the vehicle with large knives and attacked people at bars and restaurants in nearby Borough Market until they were shot dead by police.
Seven people were killed and 48 injured in the attack on Saturday, with 21 fighting for their lives in hospital.
Assistant Commissioner Mark Rowley, the Metropolitan Police head of counterterrorism, said that while police believe all the attackers were killed, the investigation is expanding.
British Transport Police said casualties were reported after an incident that may have involved a van and a knife attack, the BBC said, while the London Ambulance Service said it was sending multiple resources to the incident.
London police said officers killed the attackers within eight minutes of arriving at the scene.
At least four police vans were stationed behind a cordon outside the Elizabeth Fry flats in King's Road.
The federal government is advising Canadians to be vigilant in the wake of Saturday night's deadly terrorist attack in London.
The incident saw the assailants drive a van into pedestrians on London Bridge at about 10pm before knifing people in nearby Borough Market.
Saturday's attacks bore similarities to one in March on Westminster Bridge in London, in which a man plowed into a crowd of pedestrians, killing five, and then stabbed a police officer to death in the grounds of parliament before being shot dead.
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To Trump, that is a command performance that will nearly certainly keep him in his job. As ever, the President dismissed the allegations as the work of the "fake news media".
Iran has condemned the London terrorist attack, which left seven dead and at least 48 injured on Saturday night, adding that the recent surge in terrorism worldwide should serve as a "wake-up call" for the global community.
May then called for global agreements to regulate the internet, saying that the web affords extremism "the safe space it needs to breed". She went on to say the United Kingdom needed undertake new efforts at home, and reach new worldwide agreements with other countries to help "deprive the extremists of their safe spaces online".
May said the attacks weren't directly connected, but that "terrorism breeds terrorism" and attackers copy one another.
May said that Britain's counter-terrorism strategy would be reviewed, and warned that the internet could no longer remain a "safe space" for extremists.
The Alliance Party paused campaigning for 24 hours, while the Ulster Unionists suspended theirs "until further notice". "That's because they used knives and a truck!", he wrote in his final post for the morning before taking off for a local golf course.
Sinn Fein leader at Stormont Michelle O'Neill condemned the attacks.
German Chancellor Angela Merkel said in a statement that her thoughts were with victims and their families and that Germany "stood firmly and resolutely at Great Britain's side against every form of terrorism". "If we don't get smart it will only get worse", Trump wrote.
No terror group has claimed responsibility for the attack.
The recent attack in London should serve as a "wake-up call" for the global community to start taking an "honest and responsible" approach to terrorism and root out the "financial and ideological sources of violence", Iran's Foreign Ministry said.