Upon graduating, Burnet began work as a reporter for "The Glasgow Herald", before joining "The Economist" in 1958 as a sub-editor, leader writer, and subsequently, associate editor. He switched to television in 1963, becoming political editor for ITN. While reporting, Burnet became a relief newscaster and worked on ITN's current affairs programmes including "Roving Report", "Dateline" and "Dateline Westminster". He was also the main anchor for the ITV network's coverage of the 1964, 1966 and 1970 General Elections and the Apollo 11 Moon landing in 1969.