The London Fire Brigade (LFB) are investigating the cause of the fire that broke out in the kitchen of the Fitzrovia pub at 12.15pm on Wednesday.
They said there were no reports of any injuries in the pub the Snatch director opened last year with his Gritchie Brewing Company.
The LFB said they had the inferno under control two-and-a-half hours after being called.
Station Commander Jason Fisby said: "The fire is within the extraction system from the first floor to the roof vent. There are no reports of any injuries.
"Access to the seat of the fire is challenging and very labour intensive. The number of fire engines at the scene is a reflection of the need for a high turn over of firefighters wearing breathing apparatus.
"Firefighters are carrying out salvage work and trying to prevent water damage on the floors below."