Noble and politician. Hume-Campbell was born in Edinburgh, the second son of Alexander Hume-Campbell, 2nd Earl of Marchmont 1675 -1740). He was educated in the Netherlands and at the University of Edinburgh. Hume-Campbell entered the House of Commons in 1734 along with his twin brother Alexander (d. 1760), although, like his father, he was no friend of Prime Minister Robert Walpole, and this reduced his influence. He left parliament after inheriting the Earldom in 1740 (his older brother having died in 1724). Following Walpole's death, he sat in the House of Lords as a Scottish representative peer from 1750. He built Marchmont House as his principal home in 1754. In 1764, he was appointed Keeper of the Great Seal of Scotland, and served as a Governor of the Bank of Scotland (1763-90). He was an enthusiastic collector of rare books and manuscripts, and his collection is said to have been one of the finest and most valuable in Britain. He was a great friend of poet Alexander Pope.
Hume-Campbell died at his home in Hemel Hempstead, Hertfordshire. With his two sons having predeceased their father, the Earldom of Marchmont became extinct.