Redgrave was born on 16 July 1939 in Marylebone, London, England. He studied at the Westminster School and at King's College, Cambridge. Redgrave was married to Deirdre Hamilton-Hill from 1962 until they divorced in 1975. Then he was married to Kika Markham from 1985 until his death in 2010. They had four children. Redgrave died on 6 April 2010 in Tooting, London, England from prostate cancer, aged 70.