Four fire engines and around 25 firefighters were called to a fire at a flat on Sutton Way in North Kensington.
Part of a flat on the fourth floor of a five-storey block was damaged by the fire. One man was taken to hospital suffering smoke inhalation by London Ambulance Service crews.
The Brigade's fire investigators believe the fire was accidental and caused by the unsafe disposal of a cigarette.
A London Fire Brigade spokesperson said: "If you are a smoker, it's absolutely vital you ensure your cigarette is completely out when you've finished smoking it.
"Make sure smoking materials are cold before emptying ashtrays. Preferably wet stubs before them into a bin."
The Brigade was called at 1316 and the fire was under control by 1420. Fire crews from Park Royal, West Hampstead, Fulham and Willesden fire stations were at the scene.