Through his paternal great-grandmother, Anne Gilbert, Power was related to the actor Laurence Olivier; through his paternal grandmother, stage actress Ethel Lavenu, he was related by marriage to author Evelyn Waugh; and through his father's first cousin, Norah Emily Gorman Power, he was related to the theatrical director Sir (William) Tyrone Guthrie, founder of the Stratford Festival in Canada and the Tyrone Guthrie Theatre in Minneapolis, Minnesota.