Police and ambulance crews were called to the crash with parked vehicles on Downham Way just after 11.30am yesterday (January 7).
An ambulance crew and an incident response officer treated the driver at the scene, before being taken to hospital.
The drivers injuries are not life-threatening.
There has been no arrests.
A spokesperson for the Metropolitan Police said: “This seems to have been a car in collision with parked vehicles at around 1130hrs. No arrest. Driver taken to hospital, but injuries aren’t life-threatening.”
A London Ambulance Service spokesperson said: “We were called yesterday (7 January) at 11:31am to reports of a road traffic collision on Downham Way.
“We sent some resources to the scene, including an ambulance crew and an incident response officer.
“We treated a person at the scene, before taking them to hospital.”