The whole of the roof and first floor were ablaze at the scene in Park Road, London Fire Brigade said, after attending the scene at around 4.30pm on Thursday.
The section was damaged in the fire, as was part of an adjacent house roof. London Fire Brigade reported the fire was under control by 7.46pm.
“Fire crews from Chiswick and surrounding fire stations attended the scene,” a statement added.
The cause of the fire is under investigation.