Ten fire engines and around 70 firefighters were called to a fire at a shop with flats above on Uxbridge Road in Shepherd's Bush.
Part of a ground-floor shop and a five-roomed flat on the first floor of the building were alight. A child, a man and two women left the property before the Brigade arrived and were treated on scene by London Ambulance Service crews. Firefighters carried out salvage operations in the basement of the property to minimise damage.
The Brigade's 999 Control Officers took 22 calls to the blaze.
Station Commander David Reed, who was at the scene, said: "The fire was producing heavy smoke in the local area. Residents were advised to keep their windows and doors closed.
"Firefighters used one of the Brigade's 32-metre turntable ladders as an observation tower and thermal imaging cameras to check for fire spread.
"Uxbridge Road is closed between Devonport Road and Ingersoll Road whilst crews continue to work to make the scene safe. Please avoid the area where possible."
The Brigade was called at 1557 and the fire was under control by 1913. Fire crews from Acton, Paddington, Richmond, Wandsworth and surrounding fire stations attended the scene.
The fire is believed to have been accidental and caused by the ignition of grease within the the extraction system.