Speaight studied under Elsie Fogerty at the Central School of Speech and Drama, then based in the Royal Albert Hall, London.
He played the title role in the first broadcast in 1941-42 of the radio drama The Man Born to Be King.
He was a Roman Catholic convert, and biographer of Hilaire Belloc and Eric Gill.
He married the Welsh actress Evelyn Bowen, with whom he had a son; they separated in 1939.
Evelyn later married the celebrated Irish writer Frank O'Connor, with whom she had three children.