Zimmerman, who'll play Miranda Frayle, recently she won the 2013 Olivier Award for Best Supporting Actress in a Musical for her performance as Sheila in A Chorus Line at the Palladium. She is currently nominated for a WhatsOnStage Award for the role, winners of which are announced on Sunday.
Starring Olivier Award-winner Patricia Hodge as Felicity, Caroline Quentin as Moxie and Rory Bremner making his theatre debut as Crestwell the butler, Noel Coward's play centres on the consternation caused when a young Earl announces he is to marry a Hollywood film actress (Zimmerman).
Steven Pacey will return in the role of Peter in Trevor Nunn's production. Also returning to the production from Bath are Timothy Kightley as Admiral Sir John Hayling, Amanda Boxer as Lady Cynthia Hayling, Sam Hoare as Nigel and Rebecca Birch as Alice.
Warren Sollars (Mamma Mia!, From Here To Eternity) will lead the cast of the forthcoming UK tour of 20th Century Boy, playing the Glam Rock legend Marc Bolan.
He will be joined by TV regulars Sue Jenkins (Brookside, Coronation Street) and Luke Bailey (Waterloo Road, Casualty).
Completing the cast are Jade Albertson, Matthew Ashcroft, Lakesha Cammock, Andy Coxon, Llandyl Gove, Nathan Graham, Donna Hines, Christopher Hunt, Peter Manchester, Chris Milford, Katia Sartini, Steve Simmonds, Lucy Sinclair and Naomi Slights.
20th Century Boy is directed and choreographed by Gary Lloyd (Thriller Live), written by Peter Rowe in association with Gary Lloyd, and features the songs of Bolan and his band T-Rex.
The tour kicks off in Inverness on 18 April before visiting venues including Manchester, Birmingham, Southampton, Bristol, Belfast, Cardiff, Wimbledon and Plymouth.
Jeremy Herrin's revival of Julian Mitchell's play, first seen in Chichester last year, runs at Trafalgar Studios 1 from 26 March to 21 June 2014.
Set in a 1930s English public school, the play, a fictionalised account of the youth of such people as the spy Guy Burgess and the Communist John Cornford, centres on two outsiders, one coming to terms with his homosexuality, the other already a committed Marxist.
The cast is led by Will Attenborough, son of director Michael Attenborough, as Judd, and newcomer Rob Callender as Bennett.