Eight fire engines were called to the Famous Shop mini market and off licence in Yorkshire Street just before 9am.
The incident has now been reduced to six fire engines along with the aerial ladder platform. Firefighters are continuing to monitor and extinguish hotspots within the building. The smoke has now dissipated.
Road closures are currently in place in Plumbe Street, Church Street, Oxford Road and Yorkshire Street.
Police are urging people to avoid the area.