Prior to graduating with a degree in English from the University of Oxford in 1964, York had toured with the National Youth Theatre, also performing with the Oxford University Dramatic Society and the University College Players. After some time with the Dundee Repertory Theatre, where he played in Brendan Behan's The Hostage, York joined National Theatre under Laurence Olivier where he worked with Franco Zeffirelli during the 1965 staging of Much Ado About Nothing. Following his role on British TV as Jolyon (Jolly) in The Forsyte Saga (1967), York made his film debut as Lucentio in Zeffirelli's The Taming of the Shrew (1967). He then was cast as Tybalt in Zeffirelli's 1968 film adaptation of Romeo and Juliet. He starred in The Guru (1969), then played an amoral bisexual drifter in Something for Everyone (1970). In the 1971 film Zeppelin, he portrayed a World War I soldier with conflicted family loyalties who pretends to side with the Germans. He portrayed the bisexual Brian Roberts in Bob Fosse's film version of Cabaret (1972). In 1975 he portrayed a British soldier in 19th century colonial India in Conduct Unbecoming, the first of three movies he did with director Michael Anderson. In 1977, he reunited with Franco Zeffirelli as John the Baptist in Jesus of Nazareth.