Six fire engines and around 40 firefighters were called to a flat fire on Trebovir Road in Earl's Court.
Part of two flats on the third and fourth floors of the building were alight.
The Brigade's 999 Control Officers took 15 calls to the blaze.
Station Commander David Reed, who was at the scene, said: "Crews arrived to find a well-developed fire. Eight people left the building before the Brigade arrived and one woman was treated on scene by London Ambulance Service crews.
"One of the Brigade's 32-metre ladders was used as an observational tower.
"Trebovir Road is closed from the junction of Earl's Court Road and Nevern Square, whilst firefighters continue to damp down.
"Crews are expected to remain on scene this afternoon, alongside fire investigators who are working to determine the cause of the fire."
The Brigade was called at 1207 and the fire was under control by 1417. Fire crews from Chelsea, Kensington, Hammersmith and surrounding fire stations attended the scene.
The cause of the fire is under investigation.