Burnside, a well-known human rights activist and lawyer, attended Melbourne Grammar School and received a Bachelor of Laws from Monash University in 1973. He was made a Queen's Counsel in 1989, and acted for the Maritime Union of Australia during the 1998 Australian waterfront industrial dispute.
From this point on, Burnside began to undertake more pro bono work relating to human rights issues, and was a staunch opponent of former Prime Minister John Howard's mandatory detention of asylum seekers. He also represented Bruce Trevorrow, an Aboriginal member of the Stolen Generations, who successfully sued the South Australian Government for removing him from his family.
In 2004, Burnside was awarded the Human Rights Law Award by the Human Rights and Equal Opportunity Commission. In 2009, he was made an Officer of the Order of Australia for services as a human-rights advocate.
Burnside is a patron of numerous arts organisations and has also published books on Internet law and philology.