Desmond was born in Cork in 1935, and was educated at the Colaiste Chriost Ri, the School of Commerce and University College Cork. He became a trade union official with the ITGWU (known later as SIPTU) and the Irish Congress of Trade Unions. His father Cornelius (Con) was Lord Mayor of Cork from 1965–66.
At the 1969 general election he was elected Labour Party Teachta Dála (TD) for Dún Laoghaire and Rathdown. From 1981–1982 he served as Minister of State at the Department of Finance. In 1982, after Michael O'Leary's resignation as Labour Party leader, Dick Spring was elected as the party's new leader and Desmond was chosen as his deputy.
The Fine Gael-Labour Party coalition was returned to power in the November 1982 general election, and when the 24th Dáil meet in December, Garret FitzGerald was appointed as Taoiseach on the Dáil's nomination. Desmond was appointed Minister for Social Welfare and Minister for Health. He resigned from his ministerial posts on 20 January 1987, along with the other Labour ministers, bringing about the collapse of the government.
At the 1987 general election, Desmond was returned to the 25th Dáil, when Fianna Fáil returned to power. He did not contest the 1989 general election, and on 15 June 1989 he was elected as a Labour Member of the European Parliament (MEP) for Dublin. He was a member of the European Court of Auditors from 1994 to 2000, being replaced by Máire Geoghegan-Quinn.
He was elected president of the Maritime Institute of Ireland on 18 November 2006. He remains a member of the Council of the Maritime Institute of Ireland. As president he oversaw the revision of its articles of association and the securing of €3.2 million funding for the restoration of Mariners' Church, Dún Laoghaire, which houses the National Maritime Museum of Ireland.
- Desmond, Barry (June 2009). No Workers' Republic - Reflections on Labour and Ireland 1913–1967. Dublin: Watchword. ISBN 978-0-9557249-3-0.
- European Parliament profile
|Minister for Social Welfare
|Minister for Health