The son of a livery-stable keeper in Westminster, John Hinchliffe attended Westminster school before entering Trinity College Cambridge in 1750 (pensioner, B.A. 1754, Fellow 1755, M.A. 1757, D.D. 1764); he was ordained in 1757. Hinchliffe returned to Westminster School where he was assistant master (1757-64), and head master (1764); afterwards he was master of Trinity College Cambridge (1768-88). Hinchliffe was vice-chancellor of Cambridge (1768) and Bishop of Peterborough (1769-94).
A sermon preached before the Lords spiritual and temporal. 1773.
A sermon preached before the Society for the propagation of the Gospel. 1776.
A sermon preached in the cathedral church of St. Paul. 1786.