Four fire engines and around 25 firefighters were called to a fire on Longlands Court in Westbourne Grove.
Half of the balcony of a six-roomed flat on the third floor was damaged by the fire. There were no reports of any injuries.
The Brigade was called at 2043 and the fire was under control by 2116. Fire crews from North Kensington, Kensington and Paddington fire stations attended.
The cause of the fire is under investigation.