Events from the year 1745 in Great Britain.
- 23 January – William Jessop, civil engineer (died 1814)
- February – Samuel Hearne, explorer, fur-trader, author and naturalist (died 1792)
- 2 February
- 14 February – Lady Sarah Lennox, courtier (died 1826)
- 20 February – Henry James Pye, poet laureate (died 1813)
- 4 March – Charles Dibdin, composer (died 1814)
- 12 May – William Creech, Scottish bookseller and Lord Provost of Edinburgh (died 1815)
- 13 July – Robert Calder, admiral (died 1818)
- 20 July – Henry Holland, architect (died 1806)
- 20 or 21 August – Francis Asbury, bishop of the Methodist Episcopal Church (died 1816 in the United States)
- 17 October – William Scott, 1st Baron Stowell, judge and jurist (died 1836)
- 7 November – Prince Henry, Duke of Cumberland and Strathearn, member of the royal family (died 1793)
- 10 December – Thomas Holcroft, writer (died 1809)
- 26 February – Henry Scudamore, 3rd Duke of Beaufort (born 1707)
- 18 March – Robert Walpole, first Prime Minister of Great Britain (born 1676)[8]
- 28 May – Jonathan Richardson, portrait painter, writer on art and collector (born 1667)
- 30 September – Sir John Baird, 2nd Baronet, Scottish politician (born 1686)
- 19 October – Jonathan Swift, Irish satirist (born 1667)
- 16 November – James Butler, 2nd Duke of Ormonde, exiled Irish-born statesman and soldier (born 1665)
- John Freame, banker (born 1669)
Palmer, Alan; Palmer, Veronica (1992). The Chronology of British History. London: Century Ltd. pp. 217–218. ISBN 0-7126-5616-2.