He was educated at Eton and at Brasenose College, Oxford, and called to the bar at the Middle Temple in 1813.
He sat in the House of Commons of the United Kingdom from 1816 to 1822. The seat was a pocket borough which had been dominated since the 16th century by the Luttrell family, who owned the feudal barony of Dunster. The Fownes Luttrell brothers were re-elected unopposed in 1818 and 1820, but Henry resigned his seat in 1822 to become a Commissioner of the Board of Audit.
They covered more than 15,000 acres (6,100 ha), and at the time yielded an income of over £20,000 per annum (equivalent to £17 million in 2016).
Henry died unmarried on 6 October 1867, aged 77.
5th United Kingdom Parliament. 6th United Kingdom Parliament. 7th United Kingdom Parliament]
His father died on 16 February 1816, and on 12 March Henry was elected unopposed to his father"s parliamentary seat as Member of Parliament (Member of Parliament) for Minehead.