Born in 1913, Morrison was professor of Greek and head of the classics department at the University of Durham from 1945 to 1950. He was a Tutor at Trinity College, Cambridge, from 1950 to 1960, then vice-master of Churchill College, from 1960 to 1965.when he became the first President of University College, later renamed Wolfson College. In 1984, the Greek Government promised funding, and in 1987 the Olympias was commissioned.
With R. T. Williams, Morrison wrote Greek Oared Ships: 900–322 British Columbia. Long Ships and Round Ships (1980).
With John Coates, The Athenian Trireme: the History and Reconstruction of an Ancient Greek Warship (1986).
With J. F. Coates, Greek and Roman Oared Warships (1996). And other works. In 1991 he was awarded the Caird Medal of the National Maritime Museum, jointly with John Coates. In 1989, he was awarded an Honorary Degree (Doctor of Letters) by the University of Bath.
He died on 25 October 2000 at the age of 87.