He was the son of Thomas Warburton of Winnington Hall by his wife Anne, second daughter of Sir Robert Williams, 2nd Baronet, of Penrhyn. Thomas Warburton was the son of Sir George Warburton, 1st Baronet, of Arley, by his second wife Diana, daughter of Sir Edward Bishopp, 2nd Baronet, of Parham. Hugh's sister Jane married John Campbell, 2nd Duke of Argyll.
Warburton joined the Army as a cornet on 25 July 1715. On 24 January 1734 he was made lieutenant-colonel of Lord Mark Kerr's Regiment of Dragoons, and on 3 June 1745 colonel of the 45th Regiment of Foot. After King George's War, the regiment was stationed in Halifax throughout Father Le Loutre's War and the French and Indian War. On 24 September 1761 he transferred from the 45th to the colonelcy of the 27th Regiment of Foot, which he would hold until his death on 26 August 1771. He was promoted to major-general in 1755, lieutenant-general in 1758 and general on 13 April 1770.
Warburton married Susanna, daughter and co-heiress of Edward Norris, of Speke. Their only child, Anne Susanna, married Richard Pennant, 1st Baron Penrhyn, but they had no children. After her husband's death Lady Penrhyn sold Winnington Hall to Sir John Thomas Stanley, 7th Baronet, of Alderley; she died on 1 January 1816.
- "Person Page". Thepeerage.com. Retrieved 2016-12-29.
- George Ormerod, The History of the County Palatine and City of Chester, vol. 2 (1819) p. 111.
- John Burke and John Bernard Burke, The Extinct and Dormant Baronetcies of England (1838) p. 551.
- British Army List for 1740, p. 11.
- Frederic Boase, "An English Army List of 1740" in Notes and Queries, 12th series, vol. 2, no. 36 (2 September 1916) p. 193.
- "No. 8444". The London Gazette. 25–29 June 1745. p. 2.
- "No. 9459". The London Gazette. 15–18 March 1755. p. 2.
- "No. 9759". The London Gazette. 21–24 January 1758. p. 1.
- "No. 11039". The London Gazette. 1–5 May 1770. p. 1.
- [S37] Mosley, Charles, editor. Burke's Peerage, Baronetage & Knightage, 107th edition, 3 volumes. Wilmington, Delaware, U.S.A.: Burke's Peerage (Genealogical Books) Ltd, 2003.
| Colonel of the 45th Regiment of Foot
The Lord Blakeney
| Colonel of the 27th Regiment of Foot
Sir Eyre Coote
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