Four fire engines and 21 firefighters and officers were called to a fire at a block of flats in Hillside, Stonebridge.
Part of a five-roomed flat on the fifth floor was damaged in the fire. A woman and a child left the property before the Brigade arrived. They were taken to hospital by London Ambulance Service crews suffering smoke inhalation.
The Brigade was called at 1038 and the fire was under control at 1138. Fire crews from Park Royal, Stanmore, Wembley and North Kensington fire stations attended the scene.
The cause of the fire is under investigation.