Four fire engines and around 25 firefighters were called to a fire at a flat on Evenwood Close in Putney.
Part of a five roomed flat on the second floor of the building was damaged by fire. A small part of the balcony of another flat on the second floor was also damaged by fire. Two men left the building before the Brigade arrived. They were treated on scene after suffering from smoke inhalation.
The Brigade's 999 Control Officers took 14 calls to the fire.
The Brigade was called at 0443 and the fire was under control by 0606. Fire crews from Wandsworth, Fulham, Battersea and Chelsea fire stations attended the scene.
The cause of the fire is under investigation.