Mirren earned the Best Actress prize for her portrayal of Britain's Queen Elizabeth II in "The Audience," the BBC reported. She previously won an Oscar for the same role in the film, "The Queen."
Lester and Kinnear shared the Best Actor accolade for their performances as Othello and Iago in "Othello."
"Chimerica" by Lucy Kirkwood was named Best Play and Stephen Sondheim's "Merrily We Roll Along" Best Musical, the BBC said.
The Theatre Icon Award went to Maggie Smith.
"Homeland" star Damian Lewis served as host of the awards show Sunday.