Anthony's childhood was made difficult by her mother's manic depression and schizophrenia and she left home at 19. In 1980, at age 16, Anthony was heralded as the "Face of the Eighties" by Photographer David Bailey. She was a successful model before she became known as an Actress at the age of 20. During the decade, she appeared in numerous music videos for artists such as Bryan Adams ("Summer of '69", "Somebody", "Heaven", and "Run to You"), Depeche Mode ("I Feel You"), and Simian Mobile Disco ("Cruel Intentions").

Anthony married Dutch Artist and Entrepreneur Luc Leestemaker in 1990; they divorced in 1995. She was later married to American film Director David Price for two years until they divorced. Anthony was in a relationship with Composer Simon Boswell, with whom she has a son, from 2004 to 2010. In 2008, her son was diagnosed with Juvenile arthritis. She now raises funds for research.

In 2008, Anthony guest starred as Clara Harris in the Doctor Who audio adventure Assassin in the Limelight. In February 2010, it was announced that she would be returning to the world of Dark Shadows starring in the audio drama Kingdom of the Dead.

Her television appearances in 2006 included guest lead roles in Casualty and a new sitcom pilot, Baggy Trousers. She also played the roles of Rachel Heath, a semi-regular character in The Bill and Veronica Cray in The Hollow, a two-part Poirot film for ITV. She also appeared briefly in Coronation Street on 13 August 2010 and as an American patient in Holby City in February 2013. In 2014, she appeared on an episode of Pointless Celebrities and won it, partnered with Christopher Timothy.

In February 2016, Anthony began appearing in the Channel 4 soap opera Hollyoaks as Marnie Nightingale.

In The Sunday Times on 15 October 2017, Anthony made public allegations that Harvey Weinstein had raped her in the late-1980s.

Anthony's numerous credits include British Telecom In phones advert (non speaking part) ITV's Murder in Suburbia, Agatha Christie's Poirot, a regular role in the award-winning soap opera Night & Day (ITV), Hotel! for Channel 5, BBC's Jonathan Creek, Oliver Twist, Dombey and Son, A Ghost in Monte Carlo, Campion episode Sweet Danger (as Lady Amanda Fitton), Lovejoy, Hollyoaks and ITV’s Auf Wiedersehen, Pet. She also starred for four years in the BBC sitcom Three Up, Two Down. She is also memorable for portraying Angelique Bouchard for eight episodes of the prime time revival of the gothic soap opera Dark Shadows, in which she spoke with a French accent. She also played Miss Clarise Mimsers in The Dead Man's Gun in 1998 as well as Miss Scarlett in the third series of Cluedo on ITV in 1992.