Born in Cork into a family of Travellers and street singers, she taught herself how to play the zither banjo and the fiddle at a young age. At the age of sixteen, after a family disagreement, Margaret left home and started performing as a street musician.
In the early 1950s she moved to London. With her flamboyant delivery and idiosyncratic banjo-playing, Barry became well known in the pubs and clubs of Irish London in the 1950s and '60s, frequently accompanied by the fiddler Michael Gorman. The duo was an important part of London's Irish community. Barry's singing and banjo playing became a main influence on the younger generation of ballad singers in Ireland and the UK, including Luke Kelly. One song for which she was particularly noted was "She Moved Through the Fair". Asked by interviewer Karl Dallas how she had learned it—through her family or from other Travellers, she replied cheerfully, "Oh, no. I got it off a gramophone record by Count John McCormack".