The Met Police has declared the stabbing attack a terrorist incident.
The suspect, who died at the scene, was believed to have been wearing a hoax explosive device, police said.
Mr Basu told a press conference: “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.”
British Transport Police said London Bridge station was currently closed and no trains would be stopping there.
Police have advised people near the scene to follow directions from officers on the ground.
The prime minister tweeted he was being updated on the incident and wanted to thank police and all emergency services for their response.
He is returning to Downing Street from his constituency.
Home Secretary Priti Patel also tweeted that she was “very concerned” about the incident.
Labour leader Jeremy Corbyn tweeted that the reports from London Bridge were “shocking” and his thoughts were with those who were caught up in the incident.