John Wood was born in Derbyshire, England, and was educated at Bedford School. He did his national service as a lieutenant with the Royal Artillery, where he was invalided out after being accidentally shot in the back and later almost killed in a Jeep accident.
He read law at Jesus College, Oxford. He was president of the Oxford University Dramatic Society. He had seen Sir John Gielgud as Angelo in Peter Brook's 1950 Stratford-upon-Avon production of Measure for Measure, "and suddenly knew what I wanted to do". He played Malvolio – "looking as lean, lanky and statuesque as Don Quixote," said the Oxford Mail – in a Mansfield College gardens production of Twelfth Night with Maggie Smith as Viola. He directed and starred in a student production of Richard III and invited one of the leading critics of the day, Harold Hobson, to the performance, telling Hobson that he would be "wanting in his duties" to ignore a Richard III that was "finer than Olivier’s". Out of curiosity, Hobson went to the performance, and reported that he had seen "something not to be missed"; the young actor had a "sardonic, amused condescension and visible superiority complex", and the critic foresaw "a considerable future". Wood graduated from Oxford in 1953.