• 30 March – the United Kingdom Census shows that, as part of the legacy of the Great Famine, the population of Ireland has fallen to 6,575,000 – a drop of 1,600,000 in ten years.^[1][2] This is the first census to note use of the Irish language.^[3]
• 1 August – Midland Great Western Railway extended from Mullingar to Galway.^[3]
• 7 August – Poor Relief (Ireland) Act provides for the establishment of dispensaries.^[3]
• Construction of MacNeill's Egyptian Arch, a railway bridge near Newry on the Dublin-Belfast railway line is completed.
• Tillie and Henderson open their first shirt factory in Derry.

Undated edit

• Ancestors of Presidents of the United States Barack Obama and Joe Biden migrate from Ireland to the U.S.^[4]
• Jacob's brand of biscuits, bars and coffee is founded; their first biscuit is possibly Goldgrain.

• 8 January – William McDonnell, 6th Earl of Antrim, peer (died 1918).
• 14 March – Paddy Ryan, boxer (died 1900).
• 17 March – Ted Sullivan, Major League Baseball player and manager (died 1929 in the United States).
• 21 March – Henry Prittie, 4th Baron Dunalley, peer and Lord Lieutenant of County Tipperary 1905–1922 (died 1927).
• 4 April – James Campbell, 1st Baron Glenavy, lawyer, Lord Chancellor of Ireland, first Chairman of Seanad Éireann (died 1931).
• 22 May – William Moxley, representative from Illinois's 6th congressional district (died 1938 in the United states).
• 4 September – John Dillon, land reform agitator, Irish Home Rule activist, nationalist politician, MP and last leader of the Irish Parliamentary Party (died 1927).
• 3 December – George Noble Plunkett, nationalist, politician, museum curator (died 1948).

• 23 May – Richard Lalor Sheil, politician, writer and orator (born 1791).
• 1 September – Anne Devlin, Irish republican and housekeeper to Robert Emmet (born 1780).

• Surviving 1851 Census Returns of Ireland

• 1851 in Scotland
• 1851 in Wales