Eight fire engines and around 60 firefighters were called to a fire at a block of flats on Lemon Grove in Feltham.
Part of a bin chute from the ground to the 11th floor of a 12-storey building was damaged by the fire. Around 50 people left the building before the Brigade arrived. There were no reports of any injuries.
Station Commander Jim Ryan, who was at the scene, said: "We received multiple calls to this incident and a number of people evacuated the block of flats.
"Fortunately, there were no reports of any injuries."
The Brigade's 999 Control Officers took 16 calls to the incident.
The Brigade was called at 1303 and the fire was under control by 1512. Fire crews from Feltham, Twickenham, Heston, Chiswick Southall and surrounding fire stations were at the scene.
The cause of fire is under investigation.