Hugh Downman was born at Alphington on 7 February 1740. He was the son of Hugh and Anne Downman, and cousin of the artist John Downman, ARA. He attended Exeter Free Grammar School and graduated from Balliol College, Oxford in 1763. Having trained as a priest, he then changed career and pursued medicine at both Edinburgh and Cambridge. In 1771, he was appointed one of the physicians of the Devon and Exeter Hospital, a position he held intermittently until 1805. Downman suffered chronic ill-health and was forced to resign within seven years of his initial appointment, although he was later re-instated and held the position again from 1781-1802. His deteriorating health again caused him difficulties allowing him to only hold the position for another three years until 1805.