Four fire engines and around 25 firefighters were called to a fire at a flat on Witherson Way in Eltham.
A balcony and a small part of a three roomed flat on the first floor of a block of flats was damaged by fire. One woman left the building before the Brigade arrived and was assessed on scene by London Ambulance Service.
The Brigade's 999 Control officers were called at 1842 and deployed crews from Eltham, Sidcup and Lee Green fire stations. The fire was under control by 1946.
The cause of the fire is under investigation.