Fox was born in Chelsea, London, the son of Robin Fox, a theatrical agent, and Angela Muriel Darita Worthington, an actress and writer. He is the elder brother of actor James Fox and film producer Robert Fox. He was educated at Harrow and served as a Lieutenant in the Coldstream Guards.

Fox's theatre debut was in 1958, and his first film appearance in 1963, as an extra in This Sporting Life. In the late 1960s and early 1970s he established himself with roles in major British films such as Oh! What a Lovely War (1969), Battle of Britain (1969) and The Go-Between (1970), however, it was as the assassin in The Day of the Jackal (1973) that he made his greatest impression.

From then onwards, he was much sought after, appearing in such films as A Bridge Too Far (1977) and Force 10 From Navarone (1978), with Robert Shaw and Harrison Ford. In 1978 he portrayed King Edward VIII in the television drama, Edward and Mrs Simpson.

In the 1982 film Gandhi, Fox portrayed the controversial Brigadier-General Reginald Dyer, responsible for the Amritsar Massacre in India. He then appeared as M in the unofficial 1983 James Bond film Never Say Never Again, and then with Sir Laurence Olivier in The Bounty (1984) and Wild Geese II (1985).

More recently, Fox has appeared in The Importance of Being Earnest (2002), Nicolas Nickleby (2002), and Stage Beauty (2004). He has consolidated his reputation with regular appearances on stage in London's West End.

He has received particular acclaim for his rendition of T. S. Eliot's Four Quartets at major festivals at home and abroad accompanied by the keyboard music of Johann Sebastian Bach performed by Christine Croshaw.

He was made an OBE in 2003.