The fire damaged a mezzanine floor and part of the single storey building’s roof.
Two people left before the Brigade arrived.
The Brigade - which is to stage a strike today - was called at 6.19 and the fire was under control within half and hour.
Six fire engines, 35 firefighters and officers from Wembley, Acton, Park Royal and Willesden fire stations attended the incident.
The cause of the fire is under investigation