Henn was born in Albert House, County Sligo, Ireland, and educated in Fermoy and latterly at Aldenham School, before gaining an Exhibition to St. Catharine's College, Cambridge, where he studied the Modern Languages and English triposes and was elected Fellow in 1926.
He served in the British army in the Second World War, rising to the rank of Brigadier.
He served from 1963 to 1968 as Chairman of the Central Organisation of Military Education Committees of the Universities and University Colleges, what is now the Council of Military Education Committees of the Universities of the United Kingdom (COMEC).
He gave the 1965 Warton Lecture on English Poetry.
D theses of Harivansh Rai Bachchan and David Esterly on W. B. Yeats.