He was born in Dublin, Ireland, the son of filmmaker Zelda Barron. He attended St Marylebone Grammar School, was in forms 1s, 2s and 3s, he supported Manchester United, he appeared in the film if very briefly. He made his directorial debut in 1979 and did almost all of his music videos in the 80's, including the Human League's Don't You Want Me (1981), Billie Jean by Michael Jackson (1983), Burning Up by Madonna, Take on Me by a-ha, and videos for Bryan Adams. Barron made only 8 music videos in early 90's and made his last music video in 1993 for David Bowie's "As the World Falls Down". In 1984 he directed the sci-fi comedy Electric Dreams, and then went on to direct several episodes of the television series The Storyteller before returning to the big screen, directing films such as Teenage Mutant Ninja Turtles in 1990, The Adventures of Pinocchio in 1996, Rat in 2000 and Mike Bassett: England Manager in 2001.

Barron has also directed several award winning miniseries, such as Merlin (1998), Arabian Nights (2000) and DreamKeeper (2003) for Hallmark Entertainment.