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. The family lived in the back of Haven Banks, where Cooper attended Mount Radford School for Boys, and helped his parents run their ice cream van, which attended fairs on the weekend. At the age of eight an aunt bought Cooper a magic set and he spent hours perfecting the tricks. Magic ran in his family—his brother David (born 1930) opened a magic shop in the 1960s in Slough High Street (then Buckinghamshire now Berkshire) called D. & Z. Cooper's Magic Shop. On 15 April 1984, Cooper collapsed and soon after died from a heart attack in front of millions of television viewers, midway through his act on the London Weekend Television variety show Live From Her Majesty's, transmitted live from Her Majesty's Theatre. His stage persona required that his act intentionally went wrong for comic purposes, leading to some initial uncertainty about whether this collapse was real.

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