Julie Goodyear, Janie Dee, Arabella Weir, Helen Lederer, Debbie Chazen and Jan Leeming will also star in the production at the Noel Coward theatre.
Glamour model Brook, 29, who found TV fame on The Big Breakfast, has previously appeared in the West End in Neil LaBute's comedy Fat Pig. She will replace Jerry Hall in the role of WI member Celia from November 3.
The play is based on the real life story of Napley WI, who decided to create a nude calendar to raise funds for a local cancer ward. It was adapted for the big screen in 2003, with Helen Mirren and Julie Walters starring in the movie.
Goodyear, who played Bet Lynch in Coronation Street, is cast as Cora, while Dee and Weir will play lead roles Annie and Chris.
Fellow ex-Coronation Street star James-Collier (Liam Connor) will take over from Jack Ryder as the photographer. The new cast will appear in the production until January 9.