Covington's break came in 1967 when, while still a student at Homerton College, Cambridge, she was invited to sing on David Frost's television show – after which she secured a recording contract. She followed this early success with her 1971 Godspell casting at The Roundhouse, then with her 1972 original cast recording of Godspell (Day by Day) and her role as the original Janet Weiss in The Rocky Horror Show in 1973. 1976 and 1977 saw her appearing in the two series of the television programme, Rock Follies. In 1978 she appeared with the English National Opera as Anna in The Seven Deadly Sins.