1798 in Great Britain
- 2 July – the Marine Police Force is formed on the River Thames by magistrate Patrick Colquhoun to prevent pilfering in the Port of London and West India Docks; it is the first organised police force in Britain.
- 13 July – William Wordsworth's poem Lines composed a few miles above Tintern Abbey on revisiting the banks of the Wye during a tour, 13 July 1798 is written.
- 1 August – French Revolutionary Wars: Admiral Nelson's fleet destroys the French fleet at the Battle of the Nile.
- 10 September – Battle of St. George's Caye: British settlers win a victory over Spanish settlers in what is to become the colony of British Honduras.
- 11 October – Elizabeth Inchbald's play Lovers' Vows, adapted from Kotzebue's Das Kind der Liebe, is first performed at London's Theatre Royal, Drury Lane.
- 4 December – British Prime Minister William Pitt the Younger announces the introduction of income tax in 1799.
- Newspaper Publication Act 1798 restricts newspaper circulation.
- Nathan Mayer Rothschild moves from Frankfurt in the Holy Roman Empire to England, settling up in business as a textile trader and financier in Manchester.
- The first recorded excavations at Stonehenge – among the first serious work in archaeology anywhere – are made by William Cunnington and Sir Richard Colt Hoare.
- Samuel Taylor Coleridge and William Wordsworth's anonymous collection Lyrical Ballads (including Coleridge's The Rime of the Ancyent Marinere).
- Edward Jenner's work on vaccination An Inquiry Into the Causes and Effects of the Variolæ Vaccinæ.
- Thomas Malthus' anonymous work An Essay on the Principle of Population.
- Richmal Mangnall's initially anonymous school textbook Historical and Miscellaneous Questions for the Use of Young People; this will have appeared in 84 editions by 1857.
- Regina Maria Roche's Gothic novel Clermont: a tale.
- Mary Wollstonecraft's posthumous radical feminist novel Maria: or, The Wrongs of Woman.
- March – David Hay, interior decorator (died 1866)
- 28 April – Duncan Forbes, linguist (died 1868)
- 12 June – William Abbot, actor (died 1843)
- 28 December – Thomas James Henderson, astronomer (died 1844)
- 12 May – George Vancouver, explorer (born 1757)
- 19 May – William Byron, 5th Baron Byron, dueller (born 1722)
- 19 June – William Jennens, financier, richest commoner in England (born 1701)
- 25 June – Thomas Sandby, cartographer and architect (born 1721)
- Paterson, Dick. "History – Origins". Thames Police. Retrieved 2017-04-14.
- Williams, Hywel (2005). Cassell's Chronology of World History. London: Weidenfeld & Nicolson. pp. 347–348. ISBN 0-304-35730-8.
- Everett, Jason M., ed. (2006). "1798". The People's Chronology. Thomson Gale.
- Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 0-14-102715-0.
- The Hutchinson Factfinder. Helicon. 1999. ISBN 1-85986-000-1.
- Leavis, Q. D. (1965). Fiction and the Reading Public (rev. ed.). London: Chatto & Windus.