Career
Burke sided with the Provisional Irish Republican Army in the 1970 split in Sinn Féin and the Ireland Republican Army. He served two terms in Portlaoise Prison on Ireland Republican Army membership charges in the 1970s. He was involved in anti-illegal drug trade activism in Dublin, particularly with Concerned Parents Against Drugs, and criticised the Garda Síochána for their treatment of his fellow activists. He was first elected to Dublin City Council in 1985.
In 1986 he and Tony Gregory were jailed for fourteen days for campaigning on behalf of Moore Street traders.
He was involved in negotiations during the Northern Ireland peace process in the 1990s and supported the Ireland Republican Army ceasefires. In 2010, the Sunday World newspaper was forced by the High Court to apologise to Burke for a 2007 (pre-general election) article by crime reporter Paul Williams which falsely accused him of involvement with the Ireland Republican Army. He ran for the Dáil seven times in Dublin Central but was not elected.
In June 2014, he was elected Lord Mayor of Dublin for a year.