Barrington's father was a silversmith named Henry Waldron. About 1771 young Waldron joined a troupe of actors, taking the name George Barrington. They introduced him to the pickpocket's art, and in 1773 he entered London society as a gentleman of wit and breeding. He picked the pockets of the rich at races, theatrical performances, and state ceremonies. After his eighth conviction (1790) for these crimes, he was deported to the prison settlement in Australia. There he reformed, obtained a pardon (1796), and eventually became superintendent of the convicts. He became insane a short time after retiring in 1800.

Although publishers used Barrington's name in advertisements for several histories—including A Voyage to New South Wales (1803) and The History of New South Wales (1802)—there is no evidence that Barrington wrote these works. In addition, he was said to have originated a well-known couplet concerning the exiled convicts:

These lines were actually written by an Englishman named Henry Carter in 1801 and included in a work ascribed to Barrington.