Four fire engines and around 25 firefighters tackled a balcony fire at a block of flats on Bridges Court Road in Wandsworth. Part of the balcony on the sixth floor was damaged by the blaze.
A woman was suffering from smoke inhalation and treated at the scene.
Twenty people left the building before the Brigade arrived.
The Brigade was called at 1233 and the fire was under control by 1343. Fire crews from Battersea, Chelsea, Fulham and Kensington fire stations were at the scene. The cause of the fire is under investigation.