The production, which runs from 7 February to 2 March 2013, stars the previously announced Kerry Fox, David Dawson and James Dreyfus. Fisher's casting had only been revealed in the past few days.
The 29 year-old actress, who rose to fame after winning Andrew Lloyd Webber's casting show How Do You Solve A Problem Like Maria? in 2006, has fought a long-running battle with a condition called congenital sulcus vocalis.
Speaking to the Telegraph earlier this year, she said: "I was referred to a leading American surgeon in Boston who operated on Julie Andrews and Adele. He examined me and said he would operate but that he honestly couldn’t tell whether I would ever sing again. It felt like I was spinning around in a car crash."
Although her voice was saved, her vocal range is now limited. "My voice now has a creak," she said. "I still have melody in it but I've gone from a high soprano to an alto, and that precludes certain roles in musical theatre."
Since playing Maria in The Sound of Music at the London Palladium and on tour, Fisher's subsequent theatre credits include They’re Playing Our Song at the Menier Chocolate Factory opposite Alistair McGowan and the Whatsonstage.com Award-nominated Wonderful Town at The Lowry earlier this year.
New casting for The Vortex, which is directed by Stephen Unwin, will be announced in the new year.
Coward’s savage portrayal of 1920s cocktail society centres on the tempestuous relationship between glamorous socialite Florence Lancaster (Fox) and her hedonistic musician son Nicky (Dawson), whose new girlfriend is wooed by Florence’s toyboy lover.