Duncombe was born the seventh child and fifth son of Charles Duncombe, 1st Baron Feversham and educated at Worcester College, Oxford. He was Rector of Kirby Misperton then Prebendary of Bole before his appointment as Dean. During his tenure the approach to York Minster from the south-west was widened by the construction of a spacious approach, which was named in his honour.
Duncombe married, on 13 May 1841, Lady Harriet Christian Douglas (1809-1902), the second child of Charles Douglas, 6th Marquess of Queensberry. Lady Harriet Duncombe died in London on 26 July 1902, at the age of 93. They had two sons:
- Major Alfred Charles Duncombe, JP (1843–1925), who was High Sheriff of Staffordshire in 1883; married Lady Anne Florence Adelaide Montagu (d.1940), daughter of the 7th Earl of Sandwich; and died without issue.
- Major Adolphus Montagu Duncombe, JP (1852–1904), Yorkshire Hussars; married Beatrice Dorothy Mary Bridgeman-Simpson (d.1936), daughter of Rev. William Bridgman-Simpson by Lady Frances Laura Wentworth Fitzwilliam (who was a daughter of the 5th Earl FitzWilliam); and died without issue.
- "University Intelligence". The Times (23275). London, England. 8 April 1859. p. 12.
- "Installation Of The (New) Dean Of York". The Times (23015). London, England. 9 June 1858. p. 5.
- "Death of the Dean of York". The York Herald (7161). York, England. 27 January 1880. p. 5. 19th Century British Library Newspapers: Part II
- "University and Clergical Intelligence". The Standard (2805). London, England. 6 May 1836. 19th Century British Library Newspapers: Part II.
- York Stories
- "Deans Of York". The Times (44179). London, England. 26 January 1926. p. 17.
- NPG details
- "Obituary". The Times (36831). London. 28 July 1902. p. 5.
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