He was the son of John Thornton (1720–1790) of Clapham, London, who had been one of the early patrons of the evangelical movement in Britain. At the age of five, Henry attended the school of Mr Davis at Wandsworth Common, and later with Mr Roberts at Point Pleasant, Wandsworth. From 1778 he was employed in the counting house of his cousin Godfrey Thornton, two years later joining his father’s company, where he later became a partner.
In 1784 Thornton joined the banking firm of Down and Free of London, later becoming a partner of the company which became known as Down, Thornton and Free. It was under his direction that this became one of the largest banking firms in London, with regional offices in other British cities.
In 1782 Henry Thornton had been urged to seek a seat in Parliament, and applied to contest one of the two seats for Hull. He soon withdrew on a point of principle, after learning that it was local custom to pay each voter two guineas in order to secure their vote. In September the same year Thornton was elected as member for Southwark, London. Despite lacking popular appeal, and refusing to bribe voters in a similar way to those of Hull, he became respected as a man of morals and integrity.
As an independent MP, Thornton sided with the Pittites, and in 1783 voted for peace with America. In general he tended to support William Pitt, Henry Addington and the Whig administration of William Grenville and Charles Fox. He seldom spoke in the House of Commons, as much of his contribution was in the various parliamentary committees on which he sat. In 1795 he became the treasurer of the committee responsible for the publication of the Cheap Repository Tracts.
He served on committees to examine the public debt (1798), the Irish exchange (1804), public expenditure (1807) and the bullion committee (1810), which scrutinized the high price of gold, foreign exchange, and the state of the British currency. The report of the committee, written by Thornton, argued for the resumption of gold payments in exchange for notes and deposits, which the Bank of England (of which his elder brother, Samuel Thornton, was a director) had suspended in 1797, but the recommendation was not well received at the time, and gold redemption on demand was not restored until 1821. In the next few years he continued to press for these measures to be implemented, publishing two reports in 1811.
This period 1797–1810 was a time of major change and great confusion in the British banking system, and the currency crisis of 1797 led to Thornton’s greatest contribution as an economist, for which he is most remembered today. In 1802 he wrote An Enquiry into the Nature and Effects of the Paper Credit of Great Britain, in which he set out to correct the view that the increase in paper credit was the principal cause of the economic ills of the day. This was a work of great importance, and gave a detailed account of the British monetary system as well as a detailed examination of the ways in which the Bank of England should act to counteract fluctuations in the value of the pound.