Brand plays Lonnie in the big-screen adaptation of the Broadway musical Rock of Ages.
Mirren's many stage credits include Dance of Death and Phedre. She won the Academy Award for her performance in Stephen Frears' The Queen and has received four Emmy Awards for her television work.
Both actors appeared in the Arthur film remake with Brand in the title role, as well as Julie Taymor's film version of Shakespeare's The Tempest, which starred Mirren as Prospera.
According to THR, Mirren will be examining the topic of William Shakespeare in The British, which spans 2000 years of British history.