"From 2208 hrs (local time) officers responded to reports of a vehicle in collision with pedestrians on #London Bridge".
Witnesses reported seeing two men shot by police.
A third incident had been reported in the Vauxhall area but it was later confirmed not to be connected.
The BBC reports police are searching for three potentially armed suspects.
May said that "following updates from police and security officials, I can confirm that the bad incident in London is being treated as a potential act of terrorism".
President Donald Trump touted his so-called travel ban Saturday in the wake of what authorities are calling "terrorist incidents" in London, while also pledging assistance to Britain.
Transport for London said busy London Bridge station and two others were closed at the request of police.
An eyewitness also described to CNN hearing what "sounded like" gunshots. They also issued safety instructions to those in the areas of the incidents, warning people to run, hide, and contact police when it is safe to do so.
Ciao, Schiavone? 2010 French Open champ unclear about future
Muguruza will face Estonia's Anett Kontaveit in the second round. "On clay I'm not feeling so good especially on my movement". Kiki Bertens of the Netherlands recovered from a set down to beat Australian Ajla Tomljanovic and reach the second round.
The U.K. has already been reeling from the May 22 attack in Manchester at a Ariana Grande concert that killed 22 people.
Nick Archer, who was in the London Bridge area, told Sky News: "We came out (of a bar) on to the road and looked and looked to my left and there as a guy, I thought he was just drinking but he was lying on the floor.
The injured were taken to six hospitals, while other people were treated at the scene, London Ambulance Service Assistant Director of Operations Peter Rhodes said.
Casualties were seen being taken away from Tito's restaurant on London Bridge Street with blood on the steps of the eatery. "He swerved right round me and then hit about five or six people". And then there were nearly hundreds of people coming inside. Police officers yelled at people to run from the area. The patrons sheltered in the basement and police then arrived at the scene, the witness said.
She was separated from her husband but, after eventually being able to sit up and speak, she spoke to him again and, after giving their details to police, they were allowed to leave.
Up to 20 people are feared to be injured after a van reportedly ploughed into pedestrians on London Bridge.
All three went "randomly along Borough High Street stabbing people at random", he said, adding that he witnessed a young girl being stabbed in the chest.
A witness told CNN two men had entered a restaurant in the Borough Market area and stabbed two people inside.
In March, four people were killed in London after Khalid Masood rammed his auto into pedestrians on Westminster Bridge, before fatally stabbing a policeman outside the Houses of Parliament. Five people were killed, including the attacker, and at least 40 people were injured.