The fleeing attacker, who was wearing a hoax explosive device, was tackled by members of the public before being shot by police.
Police have said say several people have stabbed, though it was not immediately clear how many people were hurt nor the extent of their injuries.
"However, as a precaution, we are now responding to this incident as thought it is terror-related".
Scotland Yard has tweeted to say officers are "responding to this incident as though it is terror-related".
Footage shows a man pinned down by police shortly before he appeared to be shot. As soon as we can provide further updates on their condition, we will. They later said that enhanced patrols would be instituted throughout the city during this busy shopping period.
An eyewitness in contact with Yahoo News UK shared a video on social media that appeared to show the moment a group of officers and members of the public held down a man on the pavement.
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Road travelers were urged to be careful, as driving conditions become unsafe amid the mix of snow, rain, ice and poor visibility. A winter storm warning for hard travel conditions in the mountains expired, but officials still urged drivers to use caution.
A number of people were stabbed by the man, said the police.
LBC listeners described hearing gunshots and one man said he saw a man shot by officers.
"Police then quickly arrived, including armed police, and then a number of shots were fired at this man".
Basu said that Khan had been living in the Staffordshire region of central England and officers were searching an address in that area.
She said the manager ran to lock the doors and staff told people to move away from the front of the restaurant. They fired two shots and killed the suspect.
"The road Cannon Street that runs down to the north end of London Bridge was being cordoned off". They were installed after the 2017 London Bridge terror attack.
London Ambulance Service has declared it a "major incident".