Burbury was born on 3 December 1909 in
Perth,
Western Australia. He was the only child of Mary Agatha (née Cunningham) and Daniel Charles Burbury. His father, born in Tasmania, was employed as a metallurgist at the
Perth Mint. Burbury's mother died two months after his birth and he was returned to Tasmania to be raised by his aunt Ada Mary Lakin in
Hobart. He contracted
poliomyelitis at a young age, leaving him with a lifelong limp. He completed his secondary education at
The Hutchins School in Hobart, where he was a prize-winning student. He went on to study law at the
University of Tasmania, graduating
Bachelor of Laws in 1932. ==Legal career==