Four fire engines and around 25 firefighters were called to a fire at an end-of-terrace house conversion on Gallosson Road, Plumstead.
Most of a first floor flat was damaged by fire. Five people left the building before the arrival of the Brigade.
The Brigade was called at 0411 and the fire was under control at 0522. Fire crews from Plumstead, Erith, and East Greenwich fire stations attended the scene.
The cause of the fire is under investigation.