The fire, which broke out on the 15th floor of 16-storey tower block Nauls Mill House, began yesterday evening.
A total of 17 response vehicles attended the scene, including 13 fire engines.
The first crew arrived at the building at 8.50pm yesterday, within two minutes of being mobilised.
Police officers and fire service personnel remain on the scene this morning.
Residents of the building have been evacuated and are in discussions with Citizen Housing about finding temporary accommodation.
Nobody is believed to have been injured in the blaze.
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