Two lorries were gutted by fire. A further lorry and four loading bays were also damaged by the blaze. Around 120 staff evacuated the building before the Brigade arrived.
The Brigade was called at 6.39 pm and the fire was under control by 8.35 pm.
Fire crews from East Greenwich, Greenwich, Deptford, Plumstead and Poplar fire stations were at the scene. The cause of the fire is under investigation.