The petite London-born daughter of a composer and a singer, Shelley was acting from an early age and was not even 10 years old when she worked in small roles in two British features, "Give Us This Day" and "Cure For Love" (both 1949). The next year, she made her professional stage debut in Southwark playing Little Nell in a production of "The Old Curiosity Shop". Her London debut did not come until five years later with "Simon and Laura". Shelley also performed in numerous revues during the next decade, before migrating to New York to do "The Odd Couple" in 1965. She stayed in the US and has become one of Broadway's most prolific actresses. She was Fay in the Broadway company of Joe Orton's "Loot" (1968), and won her first Tony nomination for her role in the ensemble piece, "Absurd Person Singular" (1975). She received a Tony for Best Actress in a Play (tying with Constance Cummings who was cited for "Wings") for her sensitive portrayal of actress Madge Kendal who befriends "The Elephant Man" (1979). She earned a third Tony nomination in the supporting category playing the assertive Maxine in "Stepping Out" (1987). Among her other notable stage credits are succeeding Dorothy Loudon as Dotty Otley the actress playing the maid in the uproarious farce "Noises Off" (1983), and as one of several actresses who played Kate, the mother, in Neil Simon's "Broadway Bound" (1987), a role in which she also toured for a year following her Broadway stint. She returned to the London stage to replace Dame Maggie Smith as Lettice in Peter Shaffer's "Lettice and Lovage" (1989-90). Back in the US, she won praise for her multiple roles in A.R. Gurney's comedy "Later Life" (1993), for succeeding Piper Laurie as the mother in Larry Kramer's searing family drama "The Destiny of Me" (also 1993), portraying Diana, the English actress first introduced to audiences in "California Suite" (and played by Maggie Smith in the film) in Neil Simon's "London Suite" (1995) and following Elaine Stritch in the role of Parthy in Harold Prince's acclaimed revival of "Show Boat" (1995-96).
Shelley's American film appearances have been limited, but she has lent her soft dulcet tones to character voices for "The Aristocats" (1971), "Robin Hood" (1974), and other films and had small roles in "Quiz Show" and "The Road to Wellville" (both 1994). On TV, she appeared in numerous "Brian Rix" farces in England and in the US was one of the participants in "A Salute to Noel Coward" on CBS. She played Lloyd Bridges' daughter in "Devlin", a 1992 Showtime original movie, and made the busted pilot "Coconut Downs" (ABC, 1991), about life at a posh hotel near a racetrack.