Cornwall was the son of Alan Whitmore Cornwall, who was archdeacon of Cheltenham from 1924 to 1932. He was educated at Marlborough College (where his older brother Alan, a county cricketer for Gloucestershire, was later to be a housemaster) and then at Oriel College, Oxford, where he studied history. He took a third-class degree in 1926.
Cornwall worked in England for four years, first at Cuddesdon Theological College in 1926–27, then as deacon in the Diocese of Durham also in 1927, as curate of St Columba's, Southwick, Sunderland in 1927–30, and as a priest in Durham in 1928.
His first posting abroad came in 1931 when he was appointed chaplain to the bishop of Colombo, Ceylon (now Sri Lanka), a position he held until 1938. He briefly returned to England for a year, as curate of St Wilfred's, Brighton in 1938–39. Thereafter came postings as a missionary priest of the Diocese of Masasi, Tanganyika (now Tanzania) in 1939–49, during which time he also served as headmaster of St Joseph's College, Chidya in 1944–49.
Cornwall was consecrated bishop of Borneo on 1 November 1949 in London, as the first to hold this post: following the devastation of World War II, the Diocese of Labuan and the Bishopric of Sarawak were merged as the Diocese of Borneo. Cornwall served as bishop based in Kuching for thirteen years until 1962, when the diocese was again divided into the Diocese of Jesselton (later Sabah) which included Labuan, and the Diocese of Kuching, which included Brunei.
Cornwall then returned to England, where he served as commissary to the Bishop of Kuching, as assistant bishop in the Diocese of Winchester, and as a canon residentiary of Winchester Cathedral from 1963 to 1973, when he retired.
Cornwall was awarded the CBE in 1955. He married Mary Dalton, daughter of the Reverend C. R. Dalton, in 1959. They had no children. Mary died in 1981.
- Cornwall, Nigel E. (1953) Borneo, past present and future, Society for the Propagation of the Gospel in Foreign Parts (SPG), 61 pp.
- Cornwall, Nigel E. (1953) "Opportunity in Borneo", East and West Review 19 (3), pp. 74–80.
- ‘CORNWALL, Rt. Rev Nigel Edmund’, Who Was Who, A & C Black, an imprint of Bloomsbury Publishing plc, 1920–2014; online edn, Oxford University Press, 2014 ; online edn, April 2014 accessed 11 Sept 2014
- Crockford's Clerical Directory 1929/30 p 275: Oxford, OUP, 1929
- St Mary's Church, Thornbury. Retrieved 27 July 2014.
- Crockfords (London, Church House, 1995) p 212ISBN 0-7151-8088-6
- Index to The Chronicle - A Quarterly Report of the Borneo Mission Association, showing many contributions by Cornwall
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