Duncombe was a younger son of Charles Duncombe, 1st Baron Feversham, and his wife Lady Charlotte, daughter of William Legge, 2nd Earl of Dartmouth.

Duncombe served in the Royal Navy and achieved the rank of admiral. Apart from his naval career he also sat as Member of Parliament for East Retford between 1830 and 1831 and 1835 and 1852 and the East Riding of Yorkshire between 1852 and 1868.

He served in the short-lived 1852 Conservative administration of the Earl of Derby as a Fourth Naval Lord.^[1] Duncombe lived at Kilnwick Percy Hall at Pocklington in the East Riding of Yorkshire.^[2] He was selected as High Sheriff of Yorkshire for 1874–75.^[3]

He married firstly Delia, daughter of John Wilmer Field, in 1836. Their eldest son, Charles Wilmer Duncombe, was a Major-General in the Army; their second son Arthur Duncombe was also a politician; while their fourth and youngest son George Augustus Duncombe was created a baronet in 1919 (see Duncombe baronets). After Delia's death in 1873 he married secondly Jane Maria, daughter of Sir James Walker, 1st Baronet. Duncombe's second wife died in August 1917. He himself died in February 1889, aged 82.

• O'Byrne, William Richard (1849). "Duncombe, Arthur" . A Naval Biographical Dictionary . John Murray – via Wikisource.

• Leigh Rayment's Historical List of MPs

• Hansard 1803–2005: contributions in Parliament by Arthur Duncombe