Hendry was born in Ipswich, Suffolk on 13 January 1931. His father, James Hendry, was born in 1901 in Glasgow. James Hendry earned a degree in Chemistry from Glasgow University before moving to Ipswich in 1924 to take up a graduate position with R & W Paul Ltd. (now BOCM Pauls Ltd). Ian's mother, Enid (née Rushton), was born in Durham in 1906. Her father, George Rushton, was an Artist and Head of the Ipswich Art School from 1906-29.

Ian's younger brother, Donald, was born on 15 August 1933. Both Ian and his brother were educated at the Ipswich School and Culford School, Suffolk. At Culford School, Ian Hendry had a keen interest in Sports, particularly boxing, cricket, running and rugby. He was also involved in amateur dramatics at Culford, helping to produce and perform in several school plays.

On leaving school in 1947, aged 16, Hendry initially embarked on a very different career, studying at the College of Estate Management in London. In 1948, he spent a year working for Bidwells at their Cambridge office. In 1949, Hendry began his National Service as part of the compulsory conscription in the United Kingdom, which was introduced after the end of World War II in 1945. He spent two years with the 32nd Medium Regiment, R.A. During this time, Hendry paced for Christopher Chataway in athletics and ran his own motorcycle stunt team. On completion of his National Service he returned to work in Estate Management.

From 1951-53, Hendry returned to work for Bidwells, but this time he was based in their Edgware office in London. During this period, Hendry re-established his interest in acting, becoming involved in Amateur theatre through a local amateur dramatics group in Edgware.

By 1953, Hendry had decided that he wanted to change his career and follow his ambition of becoming an actor. In late 1952, he had applied for a place at the Central School of Speech and Drama, London, where he was accepted and trained from 1953-55. Contemporaries at the school at that time included Judi Dench and Vanessa Redgrave, who were both two years below him; Wanda Ventham, his Future co-star in the series The Lotus Eaters, who was in the year below; and Jeremy Brett and Wendy Craig, who were in the year above him.

His 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.

As his career developed, he gained parts in films including Up in the World (1956), The Secret Place (1957) and Room at the Top (1959).

In 1960, Hendry had a part in Sink the Bismarck! (1960), before landing the lead role of Dr Geoffrey Brent in the crime series Police Surgeon.

Hendry's first marriage was to Phyllis J. Bell in September 1955, a make-up Artist who worked for Leichner, whom he first met when he began work in repertory theatre. The marriage ended in 1962. He 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.

Hendry was declared bankrupt in the late 1970s. He suffered from several health problems in his latter years, largely due to his long-term problems with alcohol which affected his professional and personal life.

His last part in a film was a substantial, though uncredited, role as a corrupt policeman in McVicar. His last public appearance was as a guest on This Is Your Life which profiled former co-star Macnee, who had been a special guest when This Is Your Life featured Hendry in March 1978.

Hendry starred opposite Nyree Dawn Porter in the TV series For Maddie With Love (1980). In 1980 Hendry starred in the film McVicar based on bank robber John McVicar (played by Roger Daltrey of rock band The Who). Towards the end of his life he had a role in the crime series Jemima Shore Investigates as the eponymous heroine's literary agent. His final TV role was in the Channel Four soap opera Brookside (1984).

On Christmas Eve 1984, Hendry died of a gastrointestinal hemorrhage in London, aged 53. He was cremated and his ashes interred in the Lily Pond beds at the Golders Green Crematorium.

He appeared in a number of films, including the Hammer entry Captain Kronos – Vampire Hunter (1974). Among the more widely seen films he appeared in during this time were Get Carter (1971), for which he received a BAFTA nomination for Best Supporting Actor, Theatre of Blood (1973) opposite Vincent Price, The Passenger (1975) and Damien: Omen II (1978).