Part of the basement of the building and the ducting (extraction system) from the basement to the fourth floor were alight. There were no reports of any injuries.
Station Commander Alan Allmark, who was at the scene, said: “There was a significant amount of smoke issuing from the basement of the building when crews arrived.
“It was a rapidly developing fire which was spreading via the ducting system.
“Firefighters worked hard to bring the fire under control and to prevent it spreading to the upper floors of the building.
“Crews will be on scene throughout the afternoon damping down and there are a number of road closures in place so we would advise motorists to avoid the area where possible as there is heavy traffic.”
The Brigade’s 999 Control Officers took eight calls to the blaze.
The Brigade was called at 12.31pm and the fire was under control by 1.37pm. Fire crews from Euston, Soho, Dowgate, Paddington, Lambeth and surrounding fire stations were at the scene.
The cause of the fire is under investigation.