Barrett was born in Brisbane, Queensland and was educated at Windsor State Primary School and at Brisbane State High School. Fascinated by radio from an early age, he won an on-air talent competition in 1939, at the age of 12: an eisteddfod that was broadcast on 4BH radio, with a musical monologue about a dog called "Paddy". This was to place him on a path different from his dream of becoming a boat-builder. In 1949, Barrett was initiated into Freemasonry as an initiate and member of Empire Lodge #197 of the United Grand Lodge of Queensland.