Baptised on 2 November 1721, Hampton was the son of James Hampton of Bishop's Waltham, Hampshire. He entered Winchester College in 1733, and was elected a scholar of Corpus Christi College, Oxford, matriculating on 20 July 1739. At Oxford Hampton was noted for his scholarship and violent behaviour, on one occasion provoking a quarrel by kicking over a tea-table in the rooms of William Collins with whom he'd been at school. He graduated B.A. in 1743, and M.A. in 1747, and took holy orders.
Lord-chancellor Henley presented Hampton, in 1762, to rectory of Monkton-Moor, Yorkshire on the basis his Polybius translation: Hampton dedicated to Henley the second edition of the work. In 1775 he obtained the sinecure rectory of Folkton, Yorkshire, which he held with his other benefice.
In 1741 Hampton began on Polybius by publishing A Fragment of the 6th Book, containing a Dissertation on Government, translated, with notes, by a Gentleman, London. This was followed by a translation of the first five books and part of the fragments (2 vols., London, 1756-61), which between that date and 1823 went through at least seven editions.
Hampton's other works were:
This article incorporates text from a publication now in the public domain: Stephen, Leslie; Lee, Sidney, eds. (1890). "Hampton, James". Dictionary of National Biography. 24. London: Smith, Elder & Co.