Four fire engines and around 25 firefighters were called to a fire at a shop with flats above on Uxbridge Road in Hayes.
Most of the first floor of the building and part of the roof was damaged by fire. The second floor of the building was destroyed by the blaze.
The Brigade's 999 Control Officers took 20 calls to the fire.
Leading Firefighter Alan Winterburn who was at the scene said: "On arrival firefighters saw smoke coming from the windows.
"A substantial amount of two floors above a shop were damaged by fire. One man left the building before the Brigade arrived and he was treated on scene by London Ambulance Service crews and taken to hospital."
The Brigade was called at 2029 and the fire was under control by 2217. Fire crews from Hillingdon, Hayes and Heathrow fire stations attended the scene.
The cause of the fire is under investigation by the Brigade and the Metropolitan Police Service.