Alcock, William Congreve (1771–1813) MP, was born in Co. Waterford, the second son of three sons and two daughters of Capt. Henry Alcock (c.1735–1812) of Wilton, Enniscorthy, Co. Wexford, landowner and MP for Waterford city (1783–1797) and Fethard, Co. Wexford (1797–9), and his second wife Elizabeth Catherine, daughter of Beverley Ussher (c.1700–1759) of Kilmeadan, Co. Waterford, MP for Co. Waterford (1735–57). Henry Alcock's politics were liberal: he was a captain in a Waterford Volunteer corps and generally voted with the opposition, supporting parliamentary reform and catholic emancipation. William entered TCD in October 1788, but there is no record of his graduation. He served as a captain of the Wexford Militia in 1796, and later became a merchant and banker in Waterford. Elected MP for Waterford city (1797–1800), he held the seat until the dissolution of the Irish parliament. Like his father, he strongly opposed the act of union, voting against it in 1799 and 1800; Cornwallis (qv) believed that he was the main instigator of opposition to the union in Waterford city. He was reelected for Waterford city in the 1801 and 1802 general elections to Westminster, but was unseated on petition in 1803.
Standing again for parliament at a Co. Wexford by-election in May 1806, he was defeated by Caesar Colclough (qv) of Tintern Abbey. In the general election of 1807 he stood again for Co. Wexford with Abel Ram (1754–1830), John Colclough (1767–1807) (brother of Caesar), and Richard Brinsley Sheridan (qv). Alcock and Ram received the loyalist vote while Colclough and Sheridan were supported by catholics and liberal protestants. During the closely fought contest Alcock and John Colclough quarrelled over the alleged poaching of votes which Alcock claimed had been promised to him. Watched by a large crowd that included the county sheriff and sixteen magistrates, the two candidates fought a duel on 30 May 1807. The duel was a bitter one: Alcock's seconds refused all attempts at mediation and he wore spectacles to compensate for his short-sightedness (which was regarded as contravening the rules of duelling). Colclough was killed in the first exchange of shots. Tried for murder at the Wexford assizes in 1808, Alcock was accused by the prosecuting counsel, Jonah Barrington (qv), of engineering the duel to ensure his election. However, the trial judge Sir William Cusack Smith (qv), a staunch tory, was sympathetic to Alcock and directed the jury to acquit him; he was duly found not guilty, and declared MP for Co. Wexford.
Deeply distressed by these events, Alcock began suffering from severe depression which developed into madness, and he was confined to Thomas Warbuton's asylum in Whitemore. His sister, Mary Anne, who had been close to Colclough, also became insane and died soon after. In 1811 Alcock's constituents petitioned for his removal, but the committee of privileges of the house of commons decided that his condition was not incurable and he remained MP for the county until the general election of 1812. His illness came to the government's attention after he demanded the entire patronage of Waterford city despite the fact he was no longer its MP. Alcock died 4 September 1813. He never married and his property devolved on his brother Henry Alcock (1792–1840), who was manager of the National Bank, Waterford, and an alderman and magistrate in Waterford city.