Horn's first academic position was in 1956 at the Department of Anatomy, University of Cambridge as a Demonstrator in Anatomy. He became a Lecturer and then a Reader, before leaving to become Professor of Anatomy at the University of Bristol in 1974.[5] In 1975, while at Bristol, he obtained his DSc degree.[5]
He remained a fellow of Sidney Sussex College after 1999 until his death; he had earlier been a fellow of King's College, Cambridge, and was elected a life fellow there in 1999.[4]