He was part of the famous Redgrave acting clan that includes his late father Michael, sisters Vanessa and Lynn, and late niece Natasha Richardson.
On stage, Corin Redgrave appeared in "A Midsummer Night's Dream," "The Tempest," "Not About Nightingales" and "Trumbo."
Among his film credits are "Four Weddings and a Funeral," "Excalibur" and "A Man for All Seasons."
"We will miss him so very much," his widow, Kika Markham, said in a statement issued to the BBC. "(He died) very peacefully (and) surrounded by his family."
Redgrave is survived by his actress daughter Jemma and his sons Luke, Harvey and Arden, the British broadcaster said.