Davenport was known particularly for his gravelly voice and — as he called them — "dodgy eyes" that came from a lazy right eye. Born Arthur Nigel Davenport, he got his start in theater as part of the English Stage Company at the Royal Court Theatre in the 1960s. During this time, he also landed small roles on the TV show The Adventures of Robin Hood and in films like Peeping Tom and The Entertainer.
One of his first breakout roles was as the 3rd Duke of Norfolk in 1966's A Man for All Seasons, followed by a memorable turn as Lord Bothwell in Mary, Queen of Scots (1971). He went on to star in The Virgin Soldiers, Play Dirty, Living Free and The Island of Dr. Moreau, among others. He also played King George II in the 1979 TV miniseries Prince Regent.
In 1981, Davenport played a member of the British Olympic Committee, Lord Birkenhead, in the inspirational sports drama Chariots of Fire, set during the 1924 Summer Olympics.
In addition to his work on-screen, Davenport also served as president of the trade union then known as the British Actors' Equity Association. Davenport retired from acting at the turn of the 21st century in part because he could no longer memorize lines.
Davenport is survived by three children, including Pirates of the Caribbean and Smash star Jack Davenport. Pirates executive producer Jerry Bruckheimer, said Jack was cast in the film in part due to his father's involvement in the 1965 pirate film High Wind in Jamaica.