Flames shot out of the balcony doors of a fourth floor flat in West Drayton.
Around 75 per cent of the property has been destroyed.
London Fire Brigade say 30 people self evacuated before their crews arrived.
Six fire engines and around 35 firefighters and officers tackled the blaze.
It is not clear whether anyone was in the flat when the fire began, but no one was injured in the blaze.
LFB was called just after 9.30am and the fire was extinguished by 11am.
The cause of the fire is under investigation.