He was educated at two schools in Essex, before entering, on 1 July 1745, Corpus Christi College, Cambridge, where he proceeded B.A.
He was later elected a fellow of his college, and in 1753 was ordained at Kew Chapel by John Thomas, the bishop of Peterborough.
He was in succession chaplain to Samuel Squire, bishop of St David's, and to John Boyle, 5th Earl of Cork.
The archbishop also appointed him master of St John's Hospital, Canterbury, and gave him a chaplaincy, which enabled him to hold his two livings.
[2] Among Duncombe's many poems, the best known were: He wrote numerous occasional pieces, such as On a Lady sending the Author a Ribbon for his Watch.