| Constituency | Dates |
|---|---|
| Coventry | 17 Nov. 1766 – 1774 |
| Midhurst | 1774 – 1780 |
| Downton | 1780 – 1784 |
Jt. clerk of the Crown King’s bench [I] 1790 – d.
Horace Walpole wrote to General Conway on 28 Sept. 1762 that his nephew Henry had ‘the genuine indifference of a Harry Conway’. He added:
Lord Beauchamp showed me a couple of his letters, which have more natural humour and cleverness than is conceivable. They have the ease and drollery of a man of parts who has lived long in the world—and is scarce seventeen.
Seymour Conway, although under age, was returned unopposed in 1766 for Coventry, a borough where his family had considerable influence. Like his elder brother, he attached himself to his uncle but sometimes took his own line. He voted with Administration over Townshend’s American proposals on 13 May 1767, although both Conway and Beauchamp voted in opposition; but voted with them on 26 May against the East India dividend bill.
The Coventry election of 1768 was contested and Seymour Conway was returned head of the poll. From now on he voted regularly with Administration but is not known to have spoken in the House. In 1774 he was returned for Midhurst as Government candidate, but in 1780 John Robinson minuted about the two Members for Midhurst: ‘Neither of these gentlemen can come in here again.’ At the contested election of 1780 he stood for Downton with Robert Shafto on Shafto’s interest. He voted against Shelburne’s peace preliminaries, 18 Feb. 1783, and for Fox’s East India bill, 27 Nov. 1783. In 1784 he again contested Downton with Robert Shafto: a double return was made, and on 19 July Shafto was declared duly elected and a new writ ordered for the second seat. But Henry made way for his brother William at the by-election. ‘Lord Henry’s disposition appears to have been always for retirement’, wrote the Gentleman’s Magazine (1830, i. 363) on his death.
He died 5 Feb. 1830.