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 announced Tuesday include Rupert Everett, James McAvoy, Mark Rylance, Rafe Spall and Luke Treadaway.
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."
Poignant drama "The Curious Incident of the Dog in the Night-Time" has eight nominations and jaunty musical "Top Hat" seven for the prizes, which celebrate London theater, opera and dance.
Winners will be announced April 28.