Six fire engines and around 40 firefighters were called to a detached house on Hanworth Road just after 10am.
Fire crews from Twickenham, Feltham and Heston fire stations attended and put the fire out in under an hour and a half.
Part of the first floor and the roof were damaged.
One man left the property before the brigade arrived and was treated at the scene for smoke inhalation.
The cause of the fire is under investigation.