Born near Chester-le-Street, County Durham in 1934, Chambers was an only child, and a poor scholar; considered "slow" by his teachers, he did not learn to read fluently until the age of nine. After two years in the Royal Navy as part of his National Service, Chambers trained as a teacher and taught for three years at Westcliff High School in Southend on Sea before joining an Anglican monastery in Stroud, Gloucestershire in 1960. He later used his experience as a monk in his novel Now I Know.
His first plays, including Johnny Salter (1966), The Car and The Chicken Run (1968), were published while he was a teacher in Stroud.
Chambers left the monastery in 1967 and a year later became a freelance writer. His works include the "Dance sequence" of six novels: Breaktime, Dance on My Grave, Now I Know, The Toll Bridge, Postcards from No Man's Land and The Pillow Book of Cordelia Kenn. He and his wife, Nancy, founded Thimble Press and the magazine Signal to promote literature for children and young adults. They were awarded the Eleanor Farjeon Award for outstanding services to children's books in 1982. From 2003 to 2006 he was President of the School Library Association.