Half of the roof of the building, in Richmond Hill, was alight, while part of the third floor of the adjoined hotel was also affected, London Fire Brigade (LFB) said.
Images on social media showed clouds of smoke and several emergency vehicles lining nearby roads on Tuesday evening.
Station manager Mike Cotton said: “Firefighters worked hard in very challenging conditions to bring the fire under control but we expect to be at the scene working throughout the day today (Wednesday) to extinguish remaining pockets of fire.
“The fire was in an annex building and had been producing a lot of smoke.
“Local road closures remain in place so we would advise drivers to avoid the area if possible and to check their journey before travelling.”
There were no reports of any injuries.
LFB said 15 fire engines attended after emergency calls were made shortly before 6.30pm on Tuesday.
The blaze was brought under control by 1.36am on Wednesday. The cause remains under investigation