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 fire service was called at 7.38pm and the fire was under control by 8.56pm. Crews from Old Kent Road, Peckham, Dowgate, New Cross, Brixton, and Lambeth fire stations attended the scene.
The fire has been recorded as accidental.