Mirren is nominated for "The Audience," alongside Hattie Morahan for "A Doll's House," Billie Piper for "The Effect" and Kristin Scott Thomas for "Old Times."
Best-actor nominees are Rupert Everett for his turn as Oscar Wilde in "The Judas Kiss"; James McAvoy for "Macbeth"; Mark Rylance for "Twelfth Night"; Rafe Spall for "Constellations"; and Luke Treadaway for "The Curious Incident of the Dog in the Night-Time."
Nominees for musicals include Michael Ball and Imelda Staunton for "Sweeney Todd," Alex Bourne and Hannah Waddingham for "Kiss Me, Kate," and Heather Headley for "The Bodyguard."
"The Curious Incident of the Dog in the Night-Time"—based on Mark Haddon's novel about a mystery-solving boy with Asperger's syndrome—has eight nominations, and jaunty musical "Top Hat" seven. The prizes celebrate the best of London theater, opera and dance.
Two political dramas—regal reflection "The Audience" and rough-and-tumble Parliamentary saga "This House"—are up for best new play, alongside love story "Constellations" and "The Curious Incident of the Dog in the Night-Time."
Best new musical nominees are geeks-made-good story "Loserville," Tina Turner tribute "Soul Sister," movie-inspired "The Bodyguard" and high-stepping "Top Hat."
Winners in most categories are chosen by a panel of theater professionals and members of the public.
Winners will be announced April 28 during a ceremony at London's Royal Opera House.