Bragg began his career in 1961 as a general trainee at the BBC. He was the recipient of one of only three traineeships awarded that year. He spent his first two years in radio at the BBC World Service, then at the BBC Third Programme and BBC Home Service. He joined the production team of Huw Wheldon's "Monitor" arts series on BBC Television. He presented the BBC books programme "Read All About It" (and was also its editor, 1976–77) and "The Lively Arts", a BBC Two arts series. He then edited and presented the London Weekend Television (LWT) arts programme "The South Bank Show" from 1978 to 2010. His interview with playwright Dennis Potter shortly before his death is regularly cited as one of the most moving and memorable television moments ever. By being just as interested in popular as well as classical genres, he is credited with making the arts more accessible and less elitist.