Burton, William Henry (1739–1818), landowner and MP, was born 16 July 1739, probably at Burton Hall, Co. Carlow, second son among four sons and two daughters of Benjamin Burton and Anne Burton (née Ponsonby). Benjamin Burton (1709–67), landowner and MP, was born 12 January 1709, the eldest son of five children of Samuel Burton (1687–1733) of Burton Hall, landowner, MP for the boroughs of Sligo (1713–14, 1715–27) and Dublin (1727–33) and high sheriff of Co. Carlow (1724), and Anne Burton (née Campbell; killed 20 October 1714 by the collapse of a scaffold at George I's coronation), daughter of Charles Campbell (1640?–1725) of Dublin, MP for Newtown, Co. Down (1661–6, 1695–9, 1703–25). After attending Eton (1725–8), he entered TCD in March 1728, but there is no record of his graduation. He was MP for Knocktopher, Co. Kilkenny (1741–60) and for Co. Carlow (1761–6), and high sheriff of Co. Carlow (1736). Married to a Ponsonby, he supported their interest in parliament, usually voting with the government; he voted for the money bill of 1753. In 1755 his father-in-law Brabazon Ponsonby (qv), 1st earl of Bessborough, requested that Burton should share the office of deputy vice-treasurer with Nathaniel Clements (qv), a move strongly supported by Archbishop George Stone (qv) to curb Clements's influence. When this was found to be unworkable, Burton was appointed a commissioner of the revenue for Ireland (7 November 1755); he also became a member of the privy council (19 September 1760). He died 1 October 1767 at Burton Hall, Co. Carlow, and was succeeded by his second son, William; his eldest son, Benjamin Burton (1736–63), MP for Co. Sligo (1757–60) and Boyle, Co. Roscommon (1761–3) and high sheriff of Co. Carlow (1760), died unmarried.
William was educated at Kilkenny College (1746) and entered TCD (1755), graduating BA (1759). He joined the army, serving as captain in the 13th Dragoons (1766–70). A popular and influential figure in Carlow politics, he was on good terms with his tenantry, often joined their celebrations, and was colonel of the Carlow Volunteers in 1783. Proprietor of Carlow borough until he sold it in 1795, he was governor of Co. Carlow (1767) and MP for Gowran, Co. Kilkenny (1761–8), and was elected six times for Co. Carlow (1768–1802). Nephew to John Ponsonby (qv), speaker of the commons, in parliament he sat with the Ponsonby faction, which generally opposed the government. He generally voted for parliamentary reform but against catholic emancipation, and seems to have rarely attended the house in the 1790s. In 1774 he was appointed barracks commissioner, and in 1784 paymaster of troops on the Irish establishment serving abroad; and in 1792 he became a trustee of the Irish linen board.
Appointed captain of the Carlow infantry yeomanry corps (31 October 1796), he was active in suppressing disaffection in Carlow. During the 1798 rebellion he expelled twenty ‘popish traitors’ (Ryan, 318) from his corps, most of whom were hanged or transported. He was a strong opponent of the act of union, voting against it in 1799 and 1800. Although the Ponsonbys were prepared to support catholic emancipation to win catholics over to the anti-union cause, Burton declared that he would not ‘vote for popery’ (Bolton, 213) under any circumstances. It is possible that he never attended Westminster, and after his defeat in the general election of 1802 he did not seek reelection. In 1806 he was appointed a commissioner of the Irish treasury (1806–7). He died 7 January 1818 in Dublin and was succeeded by his grandson William Fitzwilliam Burton (1796–1844).
He married (12 December 1765) Mary, the only child of Henry Aston of East Aston, Co. Wicklow; they had two sons, Benjamin (1766–1808) and William Henry (1767–99), and a daughter, Martha (d. 1797).