Holm was born Ian Holm Cuthbert in Goodmayes, Essex, the son of "relatively elderly" Scottish parents Jean Holm, a nurse, and Dr. James Harvey Cuthbert, a psychiatrist who worked as the superintendent of the West Ham Corporation Mental Hospital and was also a pioneer of electric shock therapy. He had an older brother, Eric. Holm was educated at Chigwell School and then the Royal Academy of Dramatic Art.