Prior to his entry into politics, Burnside was a prominent public relations consultant based in London. He was selected to fight defend the South Antrim constituency for the Ulster Unionists in a by-election in 2000 but narrowly lost to the Democratic Unionist Party. However he reversed this defeat in the 2001 British general election. Along with Jeffrey Donaldson, MP and the Rev Martin Smyth, MP, Burnside became an outspoken critic of his party leader, David Trimble's support for the Good Friday Agreement, arguing that Provisional IRA slow pace of decommissioning its arms meant that Sinn Féin, the political wing of the IRA, should not be allowed to serve in the power-sharing government.
Because of their outspoken criticism, and their attempts to depose Trimble in regularly called meetings of the party's governing Ulster Unionist Council, Burnside, Donaldson and Smyth were suspended from the UUP Parliamentary Party in 2003. However Burnside declined to follow Donaldson when he resigned from the Ulster Unionist Party in December 2003.
Supporters of Burnside see him as a potential future leader of the Ulster Unionist Party.