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She was born in the Curragh Irish Army camp, Kildare, Ireland. Her father[who?] had been active in the Irish War of Independence alongside Michael Collins. He supported the Anglo-Irish Treaty and then joined the National Army.
She grew up in Hatch Street, Dublin, attending Loreto College on St Stephen's Green and then University College, Dublin, graduating in history. The economic historian George O'Brien  supervised her MPhil in economic history, on Irish emigration to England. She went on to teach economic history in UCD for some years before moving to Southampton University with her husband, Joseph Lee. Two years after her first husband died, she remarried, to James Daly, returning to Ireland with him in 1968. They both were appointed lecturers in Queen's University, Belfast.
She soon became an activist in the civil rights movement, particularly following the introduction of internment without trial by the Stormont government. She was active in the Northern Ireland Civil Rights Association and the Northern Resistance Movement.
She was a militant member of the Prisoners' Relatives Action Committee, and the national Hunger Strike Committee. In that campaign, she worked with Seamus Costello, and soon joined him in the Irish Republican Socialist Party and the Irish National Liberation Army. After Costello was assassinated, she became chairperson, leading the party for two years. During this time she and her husband James were instrumental in opposing Sinn Féin's drift towards federalism.
According to reports in The Irish Times members of the Ulster Defence Association (UDA) had gained entry to her home with the intention of killing her husband, who was also a republican activist. Daly was captured and tied up whilst they waited for him to return home but he was in Dublin at the time and so did not arrive. After a considerable time the UDA men decided to kill Daly instead and, muffling the sound of the gun with a cushion, shot her in the head and cut the phone lines before fleeing. Her body was discovered when her ten year old daughter arrived home from school.
Daly was buried in Swords, County Dublin. Mourners at her funeral, which featured the firing of a volley of shots over her coffin, included Seán Mac Stíofáin and Ruairí Ó Brádaigh. She is included as a volunteer on the INLA monument in Milltown Cemetery and is one of several commemorated by an IRSP mural on the Springfield Road, Belfast.
- Unveiling of Memorial for Miriam Daly 3 June 2003
- IRSM Roll of Honour
- Sutton Index of Deaths: 26 June 1980, CAIN
- David McKittrick et al, Lost Lives, Mainstream Publishing, 208, p. 830
- Murals of Northern Ireland
- Straight from the Heart - an interview with Miriam Daly's widower, Jim Daly accessed 24 April 2008
- IRSP: Miriam Daly Commemoration Speech 25 June 2005 accessed 24 April 2008
- Unveiling of Daly/McNamee Plaque 22 June 2003 accessed 24 April 2008