A video posted on Twitter showed a group of about half a dozen men wrestling with someone on the ground on the sidewalk of the bridge. One of them backs away from the scene carrying a knife.
As he looks towards the melee, an armed police officer drags another person away from the man on the floor. Soon after, what sound like two gunshots ring out, and the man on the ground stops moving. Reuters could not immediately verify the footage.
London Mayor Sadiq Khan said police were not looking for anyone else in the stabbings and commended the “breathtaking heroism” of the members of public who intervened in the incident, running toward the suspect.
Mr Khan said a number of people were wounded in the incident and that some of the injuries are serious. He did not offer a figure, but said it was important to allow the families of those who were hurt some privacy.
The ambulance service declared a “major incident” in the area and London Bridge station, a busy commuter hub, was closed.
People in buildings around the scene were evacuated to the north side of the River Thames by security services.
Prime Minister Boris Johnson was on his way back to Downing Street and Assistant Commissioner Basu said he would be giving him a full briefing.
“I’m being kept updated on the incident at London Bridge and want to thank the police and all emergency services for their immediate response,” Mr Johnson said in a statement.
Cars and buses on the busy bridge were at a standstill. British Transport Police said London Bridge station, one of the city’s busiest rail hubs, was closed and trains were not stopping there.
London Bridge was the scene of an attack in June 2017 when three militants drove a van into pedestrians and then attacked people in the surrounding area, killing eight people and injuring at least 48.
Islamic State said its fighters were responsible.
The month before, a suicide bomber killed 22 children and adults and wounded 59 at a packed concert hall in the English city of Manchester, as crowds began leaving a concert by US singer Ariana Grande.
And in March the same year, an attacker stabbed a policeman close to London’s parliament buildings after a car ploughed into pedestrians on nearby Westminster Bridge.
Six people died, including the assailant and the policeman he stabbed, and at least 20 were injured in what police called a “marauding terrorist attack”.
Earlier this month, Britain had lowered its national terrorism threat level to “substantial” from “severe”, its lowest level since 2014.
Bloomberg, AAP and Reuters