Four fire engines and around 25 firefighters tackled a fire on Dursley Road in Kidbrooke.
Half of the first floor of a two-storey mid terraced house was damaged by fire. The roof of the house was destroyed by fire. There were no reports of any injuries.
The Brigade's 999 Control Officers received nine calls about the fire.
The Brigade was called at 0246 and the fire was under control by 0435. Crews from East Greenwich, Greenwich and Lea Green fire stations attended the scene.
The cause of the fire is under investigation by the Brigade and Metropolitan Police.