Alexander, Sir William (1743–1822), 1st baronet, wholesale merchant, and Dublin alderman, of Belcamp, Booterstown, and Mountjoy Square, Dublin, was born 3 March 1743, son of William Alexander (d. c.1788), wholesale merchant and linen factor, of Mary's Abbey, Dublin (originally from the city of Derry), and his wife Mary Porter of Vicardale, Co. Monaghan. William Alexander senior was granted freedom of the Dublin merchants' guild in 1732 by special grace on payment of a fine. The Alexanders, who were presbyterians, became one of the great mercantile families of Dublin.
William Alexander junior was admitted free of the merchants' guild by birth in 1763, and from 1771 to 1779 he and his father were both representatives of their guild on the lower house of Dublin corporation. In 1776–7 the son served as sheriff. He was selected as an alderman in January 1779, and served as lord mayor in 1787–8. For a period in the 1770s and 1780s both father and son were trustees of the Royal Exchange and members of the Ouzel Galley (a commercial arbitration body). Both were founder members of the Dublin chamber of commerce in 1783, and both subscribed to the Dublin Insurance Company against Fire in the 1780s, and served as governors of the Hibernian Marine Society.
By 1784 Alderman Alexander was a member of the paving commission, and two years later he was appointed to the newly established Corporation for Preserving and Improving the Port of Dublin, a position he retained till his death. In the late 1780s he was also made a lottery commissioner. These appointments reflected growing ties with Dublin Castle, a trend reinforced in 1796 when he was appointed superintendent magistrate under the Dublin police act of 1795. In this capacity he was active against the United Irishmen in Dublin in 1797–8: John (qv) and Henry Sheares (qv) were arrested by him in May 1798. He also became a lieutenant-colonel with the Royal Dublin Militia. He was a popular alderman, and his influence in Dublin corporation was a cause of suspicion to the Castle confidant, Francis Higgins (qv) (the ‘sham squire’), who accused him of building up a ‘presbyter’ party on Dublin corporation. He certainly did promote some fellow-religionists. Nevertheless, at the time of the debate over legislative union in 1799–1800, he was one of the government's most reliable (albeit ineffective) supporters in the corporation. In 1809, on the occasion of George III's jubilee, Alderman Alexander was created a baronet ‘for his public services’.
In or around 1810 Sir William Alexander founded a bank (‘Alexander's’) at 15 Upper Sackville St. The other partners were all members of his family. In 1764 he had married Catherine, daughter and heir of John Folie Mapas, barrister, of Rochestown, Co. Dublin, with whom he had two sons and two daughters. Both sons, Robert (1769–1859) and William John (d. 1856), became partners, as did Sir William's brother Robert (1752–1827), a wine merchant, a partner in Newcomen's Bank, and a former MP, and his son William James (1783–1832). On the strength of the family's commercial reputation the bank grew exceptionally fast and took on a great deal of business. However, amid many Irish banking failures in 1820 it failed in June of that year, with disastrous effects for creditors: it had liabilities of some £500,000. Sir William's house at Belcamp had to be sold. Within two years he had died, on or around 11 May 1822. His son Robert, a director of the Bank of Ireland, succeeded to the title as 2nd baronet. In 1790 his uncle, James Alexander (qv), was raised to the peerage as Baron Caledon.
In 1819 Sir William Alexander was persuaded by Dublin corporation to sit for his portrait. The picture, by Solomon Williams (1760–1824), was destroyed in a fire in the council room in 1908, but there is a reproduction in Anc. rec. Dublin, xvii, facing p. 64.