Henry Nicholas Nevile was born on 13 March 1920, the elder son of Charles Joseph Nevile (1883–1930), of Wellingore in Lincolnshire, and his wife Muriel Margaret, daughter of the diplomat Sir Nicholas Roderick O'Conor, GCB, GCMG.
As a result, Henry Nevile became heir to the estates in Wellingore and Auborn which his family had possessed since the 17th century.
In 1963, Nevile was appointed High Sheriff of Lincolnshire and the following year he became a County councillor for Kesteven, serving until 1972.
Also in 1964, Nevile became Chairman of the Upper Witham IDB; he remained in that role until 1976 and was a member until 1983, a year after he left the Lincolnshire River Board.
A liveryman of the Worshipful Company of Farmers, he served as its master between 1991 and 1992; in 1992, he was appointed a Knight Commander of the Royal Victorian Order.