The production is up for seven awards, including best new musical and best actress in a musical for Sierra Boggess.
"After The Dance," by Terence Rattigan at the National Theater, is up for six nods, including best actress, director and revival.
"King Lear" at the Donmar Warehouse has five nominations, including best actor for Derek Jacobi, director, supporting actress and revival.
The nominations were announced Monday.
This year's Olivier awards, the highest honor for London theater, will take place March 13 at Theater Royal Drury Lane.