Henrey was the son of Robert Selby Henrey- grandson of Sir Coutts Lindsay, 2nd Baronet- and the memoirist Madeleine Gal. Gal would go on to write about her son's film career in two of her many volumes of memoirs, the 1948 A Film Star in Belgrave Square and the 1950 A Journey To Vienna.
He went on to study at Downside School and Oxford University, where he obtained a degree in language and literature.
At age 25, Henrey moved to the United States, eventually settling in Greenwich, Connecticut. He and his wife Lisette had a son, Edward, a graphic artist and illustrator and a daughter, Dominique, who died from a food allergy at the age of 18, having suffered all her life from poor health.
Robert Henrey's autobiography, 'Through Grown-up Eyes: Living with Childhood Fame', was published by Polperro Heritage Press in September 2013. Henrey was interviewed on BBC Radio 4's The Film Programme in December 2015 where he discussed the impact that The Fallen Idol had on his childhood and adult life.
Henrey was cast in The Fallen Idol on the basis of a photograph of him which appeared on the dustjacket of his father's book A Village in Piccadilly. Studio head of London Films Alexander Korda passed on the photograph to director Carol Reed, who thought it exactly matched his vision of the character, Phillipe, even though the photo had actually been taken in 1942 and showed Henrey when he was three years old. Henrey's parents agreed to let him make the film and a screen test was arranged. But at the time, Henrey, by that time eight years of age, was on holiday at his grandmother's farm in Normandy. So Korda sent a plane over to France to pick him up and fly him to London for the test. Carol Reed liked him at once, especially his liquid French accent, which the part called for. Reed sat down for the first of many talks with Henrey and never saw another child. Henrey was paid £1,000 for his role, with a stipulation that if the film took more than ten weeks to make, he would be paid an extra £100 for every additional week. Because the movie took eight months to film, a long time for that era, due to Reed's exacting standards, Henrey eventually earned £5,000. When the film was released, the critics were very impressed with Henrey's performance in the film, with one calling him the greatest kid since Jackie Coogan and Henrey became a star overnight. On the strength of his performance in the film, Henrey was signed to a £30,000 contract by Sir Alexander Korda to make four more films for his company between 1948 and 1952, only one of which, The Wonder Kid, was ever made. This was filmed in late 1949 - early 1950, but not released until 1952. However, it was not a great success, influencing his family's belief that he should return to education.
Henrey worked for a number of years as a tax consulting partner at PriceWaterhouseCoopers in New York City until his retirement in 1997.
Henrey was ordained as a deacon in 1984 and went on to serve as an interfaith chaplain at Greenwich Hospital after his certification in 2001.