Four fire engines and around 25 firefighters were called to a fire at a flat in Atlip Road in Wembley.
Part of a fifth floor flat was damaged by fire.
Two people left the affected property and 10 people left the building before the arrival of the Brigade.
The Brigade was called at 0912 and the fire was under control at 1025. Fire crews from Wembley, Park Royal and Acton fire stations attended the scene.
The cause of the fire is under investigation.