Four fire engines and around 25 firefighters tackled a fire at a flat on Thurstan Street in Fulham.
A paladin bin in a lower-ground floor bin room was destroyed fire. Smoke logging affected the third to the sixth floors. Around 20 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade was called at 0042 and the fire was under control by 0143. Fire crews from Fulham, Chelsea, Battersea and Wandsworth fire stations attended the scene.
The cause of the fire is under investigation.