He was the son of composer Gerald Finzi. Like his father, the younger Finzi became a pacifist; he refused to do his National Service, and was briefly imprisoned. After his father's death in 1956, he helped his mother, Joy Finzi, to establish the Finzi Trust and sustain Gerald Finzi's reputation. Their lifestyle was bohemian, living in a remote farmhouse.
Christopher Finzi married Hilary du Pré, a flautist, in 1961, and they raised their four children in the family's home built by Finzi's parents, the composer, Gerald Finzi, and his wife Joy, an artist, at Ashmansworth near Newbury, England. DuPré's younger sister, the cellist Jacqueline du Pré, was part of the household during the 1970s. Hilary du Pré's 1997 memoir A Genius in the Family, written with her brother Piers, created a storm of controversy when it was revealed that Finzi had had an affair with his sister-in-law. The 1998 film Hilary and Jackie, whose plot was based on interviews with Hilary and Piers, told the same basic story and was also controversial.
Christopher Finzi was the elder of two sons. Both he and his younger brother Nigel (1936–2010) attended Bedales School in Hampshire, where they were exposed to a liberal education and intellectual freedom much in line with their parents' own progressive outlook on the world. Christopher Finzi attended the Royal Academy of Music and embarked on a career as a freelance cellist and became the conductor of the Newbury String Players after the death of his father who had founded the orchestra. He eventually turned his attention from music to farming, first establishing a poultry business at Ashmansworth. He and his wife operated a health food shop in Newbury.
He made several recordings in his capacity as a conductor, including a performance of Gerald Finzi's Dies Natalis and music by Robin Milford and Edmund Rubbra. From 1971 to 1997, Finzi was resident conductor of the North Wiltshire Orchestra.
- Diana McVeigh, Gerald Finzi: His Life and Music, p. 72. Retrieved 28 February 2014
- "Homepage announcement". The Finzi Trust. 28 November 2019.
- Diana McVeagh - Gerald Finzi: His Life and Music, The Boydell Press, 2005