Brannigan was born at Annitsford, the son of an organist and grandson of a miner. During his professional career, he sang as principal bass at Sadler's Wells between 1943-48, and then 1952-58. He also sang in Benjamin Britten's operas, including the premiere of Peter Grimes the parts of Noye and Bottom being written for him. Brannigan also made guest appearances at Glyndebourne and Covent Garden.
Owen Brannigan's rich ripe voice was often to be heard on radio and television, occasionally advertising Newcastle Brown Ale, or rendering folk songs, especially those of his native North East. He never fully recovered from a car accident in 1972 and died the following year. A street in Annitsford is named after him.