Witnesses told British media that the police arrived quickly at the scene soon after shots were heard.
British police shot a man on Friday after a stabbing in the London Bridge area in the center of the city, a security source told Reuters.
A 14-second video clip on Twitter filmed from a high vantage point showed what appeared to be three police officers backing away from a man lying on the pavement.
Two officers are pointing rifles at the man, who can be seen moving slightly. Reuters could not independently verify the footage.
"Police were called at 1:58 p.m. to a stabbing at (a) premises near to London Bridge," police said in a statement. "A man has been detained by police. We believe a number of people have been injured."
It is believed that somebody was stabbed and police shot a suspect, the security source said.
Sky News said a man had been shot dead. Reuters was unable to confirm that report.
Videos and photographs on Twitter showed several police cars and buses on the bridge and a truck straddling several lanes.
The ambulance service declared what it called a "major incident" in the area and London Bridge station was closed.
People in buildings around the scene were evacuated by security services to the north side of the River Thames.
"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," Prime Minister Boris Johnson said in a statement.
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.
Earlier this month, Britain lowered its national terrorism threat level to "substantial" from "severe", its lowest level since 2014.