The production, which stars Robert Lindsay, Felicity Kendal, Gary Wilmot and Sutton Foster, begans performances on 23 July for a strictly limited run until 17 October.
Other casting includes Samuel Edwards as Billy Crocker, alongside Nicole-Lily Baisden as Hope Harcourt, Carly Mercedes Dyer as Erma and Haydn Oakley as Lord Evelyn Oakleigh.
They are joined by Martin Callaghan (Ship's Purser), Jon Chew (John), Clive Hayward (Ship's Captain), Alistair So (Luke), Marc Akinfolarin, Simon Anthony, Georgie Ashford, Vivien Carter, Natalie Chua, Eamonn Cox, Jordan Crouch, Frances Dee, Charlene Ford, Selina Hamilton, Maddie Harper, Michael Lin, Robbie McMillan, Tom Partridge, Jack Wilcox, Alexandra Wright, George Beet, Gabrielle Cocca, Emily Ormiston and Liam Wrate.
Cole Porter and PG Wodehouse's classic musical is set on the SS Americana and follows two pairings that try to find love on the high seas. It features numbers such as "I Get A Kick Out of You", "You're the Top", "It's De- Lovely!" and "Anything Goes".
Kathleen Marshall, who directed and choreographed the 2011 revival, helms a brand new version of the show. The creative team also includes set designer Derek McLane, costume designer Jon Morrell, music supervisor Stephen Ridley and wig designer Campbell Young.
Anything Goes is produced by Howard Panter for Trafalgar Theatre Productions, Eilene Davidson Productions and BookMyShow.