Conway was returned for Higham Ferrers by Lord Malton on the recommendation of Sir Robert Walpole.
a young officer who, having set out upon a plan of fashionable virtue, had provoked the King and Duke [of Cumberland] by voting against the army at the beginning of the war. He was soon after, by the interest of a near relation of his, placed in the Duke’s family, where he grew a chief favourite, not only by a steady defence of military measures on all occasions, but by most distinguished bravery in the battles of Fontenoy and Lauffeld (in the latter of which he was taken prisoner), by a very superior understanding, and by being one of the most agreeable and solid speakers in Parliament, to which the beauty of his person, and the harmony of his voice, did remarkably contribute.
He voted with the Government on the Hanoverians in 1742 and 1744, but was absent on active service from the division on them in 1746, when he was classed as Old Whig.
Brought in for Penryn by Lord Falmouth as a government supporter in 1747, Conway made a number of speeches in that Parliament on military matters. Towards the end of the Parliament Horace Walpole compares him to Charles Townshend, observing that they ‘seemed marked by nature for leaders, perhaps for rivals, in the government of their country’.
He died 9 July 1795.