Part of two single-storey shops in the same building were damaged by the fire. Around 10 people left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade’s fire investigators believe the blaze was accidental and caused by a discarded cigarette.
A London Fire Brigade spokesperson said: “The fire originated in waste material which had been stored at the front of the building.
“Firefighters were faced with a well-developed fire on arrival which had spread into both shops.
“It likely that a discarded cigarette had landed amongst the waste material at the front of the premises, which included cardboard packaging, and started the blaze.
“If you’re a smoker, it’s 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 throwing them into a bin.”
The Brigade was called at 10.24am and the fire was under control by 11.18am. Four fire engines and around 25 firefighters from Southall, Ealing and Hillingdon fire stations were at the scene.