The fire broke out at around 3.45am on November 8 at the block, which is at the junction of St Peter’s Road and Charles Street. No-one was injured in the fire, which is believed to have started inside one of the flats, but residents had to be evacuated while Hampshire Fire & Rescue attended.
If you witnessed anything or have any information, police would like to speak to you.
A number of residents from adjoining roads were present and police would also like you to get in touch.
If you can help, please call 101 and quote reference 44200432989.
A 54 year old man has been arrested in connection with this incident.