McBurney was born in Stockbridge, Massachusetts, the son of Dorothy Lillian (Rundall) and Henry McBurney, and the grandson of Charles McBurney, the American surgeon (known to subsequent generations of surgeons for defining McBurney"s point). His mother was English, the daughter and granddaughter of British Army officers. His father was an American engineer
Young McBurney was home schooled. In 1933, he entered King"s College, Cambridge, reading French and German, and then Archaeology and Anthropology. Graduate studies were interrupted by war service in the Royal Air Force Volunteer Reserve (Royal Air Force Volunteer Reserve).
He completed his Doctor of Philosophy focused on studies of European flint assemblages in 1948.
In 1950, he became a British citizen. In 1952, he started as a lecturer in archaeology at Cambridge, and later Reader and finally Professor of Quaternary Prehistory.
His work included studies of the Upper Paleolithic in Britain, important excavations in the Channel Islands, extensive excavations in Libya (the Haua Fteah cave) and, in later years, excavations in Iran and Afghanistan. He also published on French prehistory, archaeological work in the Soviet Union, and on cave art
His continuing influence is felt in the work of his many pupils.
He was the father of the composer and writer Gerard McBurney and the actor and director Simon McBurney.
