Four fire engines and around 25 firefighters tackled a fire at a block of flats on Stoughton Close in Roehampton.
Half of a flat on the fourth floor was damaged by fire. Two people left the property before firefighters arrived. A man has been taken to hospital by London Ambulance Service crews suffering from smoke inhalation.
The Brigade's 999 Control Officers received seven calls about the fire.
The Brigade was called at 1603 and the fire was brought under control by 1704. Crews from Wandsworth, Richmond and surrounding fire stations attended the scene.
The cause of the fire is under investigation.