A 19-year-old woman is believed to be one of two people in a critical condition following the Kennington bus crash.
According to James Edgar, a Press Association reporter at the scene, the Met's traffic sergeant Richard Sutton said the woman was conscious but "critically ill".
According to ITV, two off-duty police officers were among the injured.
Emergency services were working to release a man and woman who are trapped on the top deck.
Mike Weston, TfL's director for buses, confirmed that the driver had swerved to avoid another vehicle. "At around 10:50 today a route 59 double deck bus, operated by Arriva, swerved to avoid another vehicle and struck a tree.
"The incident took place on Kennington Road near the Imperial War Museum.
"Our first concern is, of course, for the driver, passengers and others involved in this incident and we can confirm the emergency services are in attendance.
"There will be a thorough investigation into this incident as a matter of urgency."
Horrifying images from the scene show how the bus ploughed straight into the tree, crumpling the front of the bus.
Fire crewswere working to cut off the side of the bus.
London Fire Brigade station manager Clive Robinson, who is at the scene, said: "A number of people have been injured and are being taken care of by paramedics. Our priority now is to free those people who are still trapped and firefighters are working very hard to do that at the moment."
A statement from the Metropolitan Police said: "A number of people have been injured; we await a full assessment.
"At present, 23 people are described as walking wounded. Seven people are still being assessed, of whom two remain trapped on the bus.
"At this stage, there has been no fatality.
"There was no police vehicle involved in the collision. Two uniformed police officers were travelling on the bus, both were injured, we await further details."
A spokesman for London Fire Brigade added: "Four fire engines are on the scene from Soho, Westminster, and Lambeth fire stations. London Ambulance Service, the air ambulance, and the Metropolitan Police are also at the scene."