A long-serving member of Dublin Corporation, Dunne stood unsuccessfully as a Labour candidate for Dáil Éireann at six successive general elections, but never won a seat. He contested Dublin North East in 1965, 1969, and 1973, Dublin Artane in 1977, and Dublin North West in the 1981 and February 1982 general elections.
After his 1981 defeat, he was nominated by the Taoiseach, Garret FitzGerald to the 15th Seanad Éireann, where he served until the election of the 16th Seanad in 1982. Dunne was one of three Labour nominees who were nominated with the intention that, supported by their senate salaries, they would devote their energies to strengthening the organisation and finances of the Labour Party. The choice of Dunne was seen as a settling of old scores with the party; Dunne was an ally of the Labour leader Michael O'Leary, and his senate seat was expected to strengthen Dunne's position against Brendan Halligan, his running-mate in Dublin North West and an opponent of O'Leary's strategy of entering coalition with Fine Gael. Halligan did not stand in February 1982, but Dunne was beaten to the 4th seat in Dublin North West by Proinsias De Rossa of Sinn Féin the Workers Party.