Five fire engines and around 35 firefighters were called to a fire at a maisonette on Cambridge Square in Bayswater.
Most of a split level maisonette on the sixth and seventh floors of a seven-storey block was damaged by the fire. One person left the building before the Brigade arrived. There were no reports of any injuries.
The Brigade's 999 Control Officers took nine calls to the fire.
The Brigade was called at 1347 and the fire was under control by 1516. Fire crews from North Kensington, Chelsea, West Hampstead, Willesden, Lambeth and Paddington fire stations were at the scene.
The cause of the fire is under investigation.