Fire broke out early this morning and 15 fire engines were at the scene at the peak of the blaze. The cause of the fire is not yet known.
The building was evacuated and there were no reports of anyone being injured.
A community briefing centre was set up for the residents of the 22 flats in the block in Lambe Close, Manley Boulevard, the fire service said.
A spokesman for the fire service said: “Crews are likely to remain on the scene for some time.
“It is believed that everyone has been accounted for and a rest centre has been put in place for residents.”