The incident happened on the morning of Monday 12th November at the CLIC Sargent charity shop on Straits Parade.
Items were taken and then a fire was started at the back of the store.
DC Cowburn, investigating officer, said: ”This resulted in significant damage and the store will have to remain closed until the New Year at the very earliest.
“This was a very concerning incident as there are residential properties above the store where people were sleeping, which could have resulted in devastating consequences.”
If you have any information call 101 quoting reference number 5216251784 and speak to DC Cowburn 3646.