Downey was born and raised in Derry, County Londonderry, Northern Ireland, in 1960, in the Bogside district. Roma is named after her two grandmothers, Ro from Rose and Ma from Mary, joined together to make Roma. She attended Thornhill College, a Catholic girls school. Her mother, Maureen O'Reilly Downey, a homemaker with an interest in the performing arts, died from a heart attack at age 48 when Downey was 10 years old. Her father, Patrick Downey, was a school Teacher by training but worked as a mortgage broker. Her father died when Downey was 20. Originally, she planned to be a Painter and earned a Bachelor of Arts at Brighton College of Art. Roma studied BA(Hons) Expressive Arts at Brighton Polytechnic (which later became Brighton University). Based at the Falmer campus Downey combined Art and Drama for her degree. However, she turned her attention to acting and had a classical training attending Drama Studio London, where she performed in plays by Shakespeare, Shaw and Chekhov. She won the “Most Promising Student" of the year award.