• 1 January – Church of Ireland disestablished. St Patrick's Cathedral, Dublin, becomes the National Cathedral.
• 15 April – Ormeau Park is opened to the public by Belfast City Council.^[1]
• 16 June – The Westmeath Act is enacted allowing arrest and detention without trial.
• J. P. Mahaffy appointed to the Chair of Ancient History at Trinity College Dublin at the age of 32.^[2]

Hare coursing edit

• Waterloo Cup won by Master McGrath for the third time.

• 8 January – James Craig, 1st Viscount Craigavon, first Prime Minister of Northern Ireland (died 1940).
• 14 January – A. M. Sullivan, lawyer (died 1959).
• 16 January – Valentine McEntee, 1st Baron McEntee, Labour MP in the United Kingdom (died 1953).
• 19 January – Frederick Barton Maurice, soldier, military correspondent, writer and academic, founded the British Legion in 1920 (died 1951).
• 13 February – Joseph Devlin, Nationalist politician and MP in the British House of Commons and in Northern Ireland (died 1934).
• 30 March – William Lyle, medical practitioner and Ulster Unionist Party politician (died 1949).
• 16 April – John Millington Synge, dramatist, poet and writer (died 1909).
• 18 April – Frederick Field, Royal Navy Admiral of the Fleet and First Sea Lord (died 1945).
• ? May – Elinor Darwin, née Monsell, engraver and portrait painter (died 1954 in England).
• 17 July – J. M. Andrews, second Prime Minister of Northern Ireland (died 1956).
• 30 August – James Nathaniel Halbert, entomologist (died 1948).
• 30 November – Thomas O'Donnell, barrister, judge, Irish Nationalist, MP (died 1943).
• November – Thomas Moles, Ulster Unionist politician and journalist (died 1937).
• 26 December – Chicago May, born Mary Anne Duignan, criminal (died 1929 in the United States).

• 2 January – Samuel Blackall, soldier, politician and second Governor of Queensland, Australia (born 1809).
• 3 February – James Sheridan Muspratt, research chemist and teacher (born 1821).
• 20 February – Paul Kane, painter in Canada (born 1810).
• 1 March – Anthony Coningham Sterling, British Army officer and historian (born 1805).
• 4 July – James Duffy, author and publisher (born 1809).
• 2 October – Sir Thomas Deane, architect (born 1792).
• 6 October – Edwin Wyndham-Quin, 3rd Earl of Dunraven and Mount-Earl, peer (born 1812).
• 30 November – John T. Mills, lawyer and Supreme Court Justice for the Republic of Texas (born 1817).
• 8 December – James Murray, physician (born 1788)
• 15 December – John George, politician, judge and in 1859 Solicitor-General for Ireland (born 1804).

• 1871 in Scotland
• 1871 in Wales