A brother of the 1st Marquess of Hertford, and cousin of Horace Walpole, he began his military career in the War of the Austrian Succession.

[3] Conway was elected unopposed to the Irish House of Commons in 1741 for County Antrim, and to the British Parliament for Higham Ferrers in December 1741 on the recommendation of Sir Robert Walpole.

[3] In April 1755, he was unexpectedly appointed Chief Secretary for Ireland by William Cavendish, Marquess of Hartington, the new Lord Lieutenant.

[5] In 1761, he served in Germany as deputy to John Manners, Marquess of Granby, the British commander in the army led by Ferdinand of Brunswick.

[1] After peace preliminaries were signed at Fontainebleau in November, he supervised the embarkation of British troops from Europe, returning to England in March.

As a senior member of the Rockingham faction of the Whigs, he opposed the King's legal actions against the reformist John Wilkes in 1763[3] which resulted in his dismissal in 1764 as a Groom of the Bedchamber and as Colonel of the 1st Royal Dragoons.

[3] This led to the publication of accusation and counter-accusation in pamphlets, as it was feared that the government intended to purge the army of its political opponents.

[10] His political career came to an end in 1784 when he lost his seat in parliament due to his opposition to the new government of William Pitt and he focused thereafter on his military responsibilities retaining his post as Commander-in Chief until his complete retirement in January 1793.