Six fire engines and around 40 firefighters attended a fire at a block of flats on Summerwood Road in Isleworth.
Half of a ground-floor flat and half of a first-floor flat was damaged by fire, along with a small part of the exterior of a second-floor flat.
Around 30 people left the building before firefighters arrived and around 18 people were taken to a rest centre. There were no reports of any injuries.
The Brigade received the first of 35 calls about the fire at 2159 and Control Officers mobilised crews from Twickenham, Kingston, Chiswick, Feltham, Heston and Ealing fire stations to the scene. The fire was brought under control by 2313.
The cause of the fire is under investigation.