Eight fire engines and around 60 firefighters were called to a block of flats on Thurlow Street in Southwark.
Most of a five roomed flat on the eighth floor of a 14-storey block was damaged by the fire. Six people left the property before the Brigade arrived and were treated on scene by the London Ambulance Service.
The Brigade was called at 1938 and the fire was under control by 2056. Crews from Old Kent Road, Peckham, Dowgate, New Cross, Brixton, and Lambeth fire stations attended the scene.
The fire has been recorded as accidental.