Six fire engines and around 40 firefighters tackled a fire at an outbuilding on Hounslow Avenue in Hounslow.
A single-storey, detached outbuilding was destroyed by fire. Part of another outbuilding and two rear adjoining outbuildings were also damaged by the blaze. A man left the building before the Brigade arrived and was treated on scene.
The fire is believed to have been accidental and caused by the unsafe disposal of smoking materials.
A London Fire Brigade spokesperson said: "We'd rather you didn't smoke at all, but if you are a smoker, it's absolutely vital you ensure your cigarette is completely out when you've finished smoking it.
"If you don't, you risk causing a fire which could not only destroy properties but also cost you your life."
The Brigade was called at 2127 and the fire was under control by 2226. Fire crews from Heston, Feltham, Twickenham and surrounding fire stations attended the scene.