Four fire engines and 21 firefighters and officers were called to a fire at a block of flats in Kelmscott Gardens in Shepherd's Bush.
Part of a flat on the fourth floor was damaged by fire. One woman and a child from a neighbouring flat were led to safety via an internal staircase by crews wearing breathing apparatus and taken to hospital by London Ambulance Service
The Brigade was called at 1151 and the fire was under control at 1242. Fire crews from Hammersmith, Chiswick, Acton and Fulham fire stations attended the scene.
The cause of the fire is under investigation.