York was born in Fulmer, Gerrards Cross, Buckinghamshire, the son of Florence Edith May , a musician; and Joseph Gwynne Johnson, a Llandovery-born Welsh ex-Royal Artillery British Army officer and executive with Marks and Spencer department stores. York has an older sister, Penelope Anne and younger twin sisters, Caroline and Bridget but Bridget died a few hours after birth, according to his autobiography. He was brought up in Burgess Hill, Sussex. During his teenage years, York was educated at Bromley Grammar School for Boys, Bromley, London, Hurstpierpoint College, Sussex and at University College, Oxford. He began his career in a 1956 production of The Yellow Jacket. In 1959 he made his West End début with a small part in a production of Hamlet.