He was educated at the University of Limerick and Trinity College, in Dublin, then he worked as a journalist and a presenter.
Cox left his television programme to become a political candidate, he was elected an MEP in 1989 and he remained until 2004. During this period he was member and Vice-Chair of the Liberal and Democratic Reformist Group, member and Vice-Chair of the Group of the European Liberal, Democrat and Reform Party, member of the Delegation for relations with Australia and New Zealand, member of the Committee on Economic and Monetary Affairs and Industrial Policy, member of the Delegation for relations with Sweden, member of the Delegation to the EC-Sweden Joint Parliamentary Committee, member of the Committee on Institutional Affairs, member of the Subcommittee on Monetary Affairs, member of the Delegation for relations with South Africa, member of the Delegation to the EU-Hungary Joint Parliamentary Committee, member of the Conference of Presidents, Chair of the Parliament's Bureau, President of the Conference of Presidents and President of the European Parliament from January 2002 to July 2004.