The star, father to Jack Davenport who is currently appearing in ITV series Breathless, was also well known for his role in Oscar-winning movie Chariots Of Fire in which he portrayed Lord Birkenhead.
For many TV viewers in the late 1980s he will be best remembered for his performance as tycoon Sir Edward Frere in BBC1's Howard's Way, the popular Sunday night drama set in the wealthy yachting set.
Oxford-educated Davenport began his career as a stage actor, but in the late Fifties and Sixties he was increasingly clocking up film roles, including the dark cult movie Peeping Tom, and made a breakthrough with his performance in A Man For All Seasons in 1966.
Other films included The Virgin Soldiers and its sequel as well as Mary, Queen Of Scots and adaptations of The Picture Of Dorian Gray and Bram Stoker's Dracula.
Davenport, who died on Friday, also had guest roles in programmes such as Minder, Keeping Up Appearances and Midsomer Murders, and continued his stage work alongside his film and TV success.
He was married and divorced twice, his second to Maria Aitken, the actress and director who is mother to Jack. He had two children from his first marriage to Helena White - Hugo, a writer, and Laura, an actress.