The son of a comedy writer, he found fame as a child actor, making his debut as David Lean's Oliver Twist in 1948.
Davies died yesterday morning at his home in Blewbury, Oxfordshire.
His son William Davies said: "My father had an absolutely extraordinary career, was unfailingly supportive as a parent and will be greatly missed. He died surrounded by his family."
After various non-TV jobs, Davies joined the BBC as a production assistant in 1966.
His most notable contribution in the early days was producing the first four episodes of Monty Python's Flying Circus (1969-74) with Ian McNaughton.
He went on to produce The Goodies and Steptoe and Son before briefly leaving the BBC in the early 1970s, returning a year later.
Davies went on to produce the now classic Fawlty Towers and the entire run of The Good Life, which ran from 1975 to 1978.
He became head of comedy at the BBC in 1978, where he launched many hit shows before being promoted again in 1982, to become head of light entertainment.
Davies then moved to Thames, where he was not so prolific, although he did produce the successful Mr Bean, starring Rowan Atkinson.
By the mid-1990s, Davies had returned to the BBC, where his credits include directing a special Easter 1996 episode of The Vicar of Dibley.