Four fire engines and around 25 firefighters tackled a fire on High Street in Whitton.
One wooden shed at the rear of a a row of shops, with homes above, was destroyed by fire. Part of the fascia of the property was damaged by fire. There were no reports of any injuries.
The fire is being treated as accidental and is believed to have been caused by rubbish that was being burned.
A London Fire Brigade spokesperson said: "We would urge people to consider if burning rubbish is necessary and to take care if you’re burning waste at home or at work.
"Never leave it unattended and consider your neighbours when you do decide to have a fire. Make sure you build it well clear of buildings, garden sheds, fences and hedges and never use flammable liquids to start it or burn dangerous items such as aerosol cans. Always keep a bucket of water or a hosepipe nearby in case of fire.
"Always check your local authority’s advice and follow our safety tips."
The Brigade's 999 Control Officers received around 15 calls about the fire.
The Brigade was called at 1039 and the fire was extinguished by 1210. Crews from Twickenham, Heston, Feltham and Southall fire stations attended the scene.