Duncombe was born in London on 29 September 1729, the only child of the author and playwright William Duncombe and his wife Elizabeth née Hughes. He was educated at two schools in Essex, before entering, on 1 July 1745, Corpus Christi College, Cambridge, where he proceeded B.A. in 1748 and M.A. in 1752. He was later elected a fellow of his college, and in 1753 was ordained at Kew Chapel by John Thomas, the bishop of Peterborough. On the recommendation of Archbishop Thomas Herring, he was appointed to the curacy of Sundridge in Kent.[2]
He wrote numerous occasional pieces, such as On a Lady sending the Author a Ribbon for his Watch.[2][3]
As an antiquarian, he wrote:
Historical Description of Canterbury Cathedral, 1772
A translation and abridgment of John Battely's Antiquities of Richborough and Reculver 1774
History and Antiquities of Reculver and Herne, and of the Three Archiepiscopal Hospitals at and near Canterbury, contributed to John Nichols's Bibliotheca Topographica Britannica, vols 1 and 4 (1780).[2]