The BBC cited a government source as saying that two members of the public had died following the attack.
The source gave no further information, the broadcaster said, while the police did not immediately confirm the deaths or give the number of casualties.
The attack was “declared as a terrorist incident” but police were keeping an open mind on the possible motive, Neil Basu, head of Britain’s counter-terrorism policing, told reporters earlier.
The male suspect who was shot dead on London Bridge was wearing a “hoax explosive device,” Basu said.
Prime Minister Boris Johnson said that Basu had briefed him on the attack later on Friday.
“This is an appalling incident and all my thoughts are with the victims and their families,” Johnson tweeted.
Basu said that the police were called just before 2 pm (1400 GMT) “to a stabbing at a premises near to London Bridge.
“A male suspect was shot by specialist armed officers from City of London Police and I can confirm that this suspect died at the scene.
“Our heartfelt sympathies go out to those anxiously awaiting news from loved ones.”
The Guardian and other media said five people were injured.
Basu said that counterterrorism officers from London’s Metropolitan Police are leading the investigation and “retain an open mind as to any motive.
“We believe a device that was strapped to the body of the suspect is a hoax explosive device,” he said.
Police were still searching the area “to ensure there is no outstanding threat to the public,” Basu said.
The bridge was closed and London Ambulance Service declared a “major incident,” while city Mayor Sadiq Khan said he was in close contact with the police.
“We must – and we will – stay resolute in our determination to stand strong and united in the face of terror.
“Those who seek to attack us and divide us will never succeed,” Khan said in a statement.
The police appealed to the public to “use common sense and restraint” in sharing images of the incident online.
Some social media users had posted footage of armed police “apparently pulling civilians off a person lying on the ground on the bridge before firing at him from close range,” The Guardian reported.
BBC reporter John McManus said he saw a “fight” on the bridge, with several people attacking one man until police arrived and fired several shots at the man.