Eight fire engines, along with an aerial ladder platform, were called to the Famous Shop mini market and off licence in Yorkshire Street just before 9am on Saturday.
The fire is believed to have started in a flat above the shop premises. Nobody was injured.
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Yorkshire Street, Plumbe Street, Church Street and Oxford Road were closed until around 6pm while firefighters extinguished hotspots within the building.
The fire service are now carrying out an investigation to determine the cause of the blaze.