Born in Caerphilly, South Wales, at 19 Llwyn Onn Street, Trecenydd, Cooper was delivered by the woman who owned the house in which the family was lodging. His parents were Welsh-born army recruiting sergeant father Thomas H.

(Tom) Cooper, and his English-born wife Gertrude (née Gertrude C. Wright) from Crediton, Devon. In light of the heavily polluted air and the offer of a job for his father, the family moved to Exeter, Devon, when Cooper was three and gained the West Country accent that was part of his act.