Born in Cornwall, Craze went into acting quite by chance. At the age of twelve, he discovered through Boy Scout Gang Shows that he had a perfect boy soprano voice. This won him parts in The King and I and Plain and Fancy, both at Drury Lane, and Damn Yankees at the Coliseum. Once he had left school, he went into repertory and got into TV through his agent. His first television role was in a show called Family Solicitor for Granada which was followed, amongst others, by a part in ABC TV's 1960 series Target Luna (written by Malcolm Hulke and Eric Price and produced by Sydney Newman).