Blunn joined the Australian Public Service at the age of 21, after four years with a firm of solicitors in Melbourne. In 1979, Blunn took a position in the Department of Finance, in an area linked with works, mainland Territories, defence and other areas. He moved to the Department of Business and Consumer Affairs in 1980, and was appointed to his first permanent Secretary role in 1981 as head of the Department of the Capital Territory.
Blunn was appointed Secretary of the Attorney General"s Department in 1998, replacing Mr Stephen Skehill who resigned from the role.
Blunn retired from the public service in December 1999. In 2000, Blunn was appointed chairman of the company in charge of managing Bruce Stadium.