Hendry's professional acting career began in 1955, working in repertory at the Hornchurch Theatre in Station Lane. He was also seen in Goldoni's Servant of Two Masters at the Edinburgh Festival. In 1957, Hendry spent another season in repertory, performing in several plays at the Oxford Playhouse, Oxford. In December 1957, Dinner with the Family transferred to the West End, playing at the New Theatre, London.
Hendry's first marriage was to Phyllis Joanna Bell, née Chaddock, in September 1955. Phyllis preferred to be known as 'Jo' - an abbreviation of her middle-name - and worked as a make-up artist for Leichner. The marriage ended in 1962. Hendry married actress Janet Munro on 16 February 1963. They had two daughters, Sally and Corrie, but their turbulent life together ended in divorce in 1971. Munro died a year later in London from the heart condition myocarditis. This was a contributory factor in Hendry's increasing dependence on alcohol. Hendry later married Sandra (Sandy) Jones on 27 May 1975, with whom he had another daughter, Emma.