Four fire engines and 21 firefighters and officers were called to a fire at a shop with flats above in High Street, Hounslow.
Crews discovered a fire at the rear of the building in an area where cardboard was stored for waste collection.
Part of the ground floor shop was damaged by fire. One person left the premises before the arrival of the Brigade.
The Brigade was called at 0006 and the fire was under control at 0124. Fire crews from Heston, Twickenham and Feltham fire stations attended the scene.
The cause of the fire is believed to be accidental and due to discarded smoking materials.