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A petrol-soaked rag was set alight and stuffed through the letter box of a Herne Bay off-licence early on Tuesday.
The arsonists attacked Bay Wines in the High Street at 1.30am.
Fire crews managed to contain the fire to the front entrance.
Police spokesman Jo Robertson said: “We are now looking through CCTV footage and are appealing for any witnesses to come forward.”
Anyone with information should contact Canterbury Police on 01227 762055.