The attackers stabbed pedestrians after mowing down up to 20 people with a white van on London Bridge around 10pm last night - with up to seven people feared dead.
One witness told Reuters that she saw what appeared to be three people with knife wounds and possibly their throats cut.
Reports surfaced that a vehicle mowed down pedestrians on London Bridge, according to Sun Newspaper.
More than one person was killed when a van mowed down pedestrians on London Bridge late Saturday, British police said.
Armed police officers were sent to the scenes and shots were fired. They say that they were then alerted to stabbings in Borough Market and are now responding to an incident in the Vauxhall area.
The two incidents are being described as terrorist attacks that were taken out in coordination.
Police said they were dealing with an incident but gave no further details.
According to multiple media outlets, police are seeking three male suspects in the incident.
May's office said she was "in contact with officials and is being regularly updated on the incident at London Bridge".
"Officers are now responding to an incident in the #Vauxhall area", the statement added.
He wrote: "Whatever the United States can do to help out in London and the U.K, we will be there - WE ARE WITH YOU".
The city transit authority Transport for London has closed the bridge and ordered the London Bridge station evacuated. Witness Elsbeth Smedley told CNN that a man ran into Elliot restaurant in Borough Market and stabbed two people before running out.
"We saw injured people on the road, injured people on the pavement", he said.
However, police confirmed that they arrested a man in connection with a stabbing, but it was not related to the terror attacks in the London Bridge area. Witnesses told the BBC that a white van, traveling around 50 miles per hour, mounted the sidewalk and struck as many as six people.
The current London Bridge opened in 1973 and is made of concrete and steel.
Eyewitnesses reported panic in the vicinity of the attacks, close to a major transport hub and in an area packed with restaurants and bars.
Police rush to an incident on London Bridge in London, Britain.
The attack came on the eve of a benefit concert Grande is scheduled to play in Manchester on Sunday in aid of the victims and their families.