The role earned her a Best Actress award at the 1988 Cannes Film Festival, shared with her co-stars Barbara Hershey and Linda Mvusi.
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Notable roles have included Alice Munro in Michael Mann's The Last of the Mohicans, Lea Papin in Sister My Sister, Florence Banner in Tipping the Velvet, Anne Boleyn in the first adaptation of The Other Boleyn Girl, and Sabina Spielrein in the play The Talking Cure.
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In August 2005, May appeared in Blackbird by David Harrower alongside Roger Allam at the Edinburgh Festival in a production by German star director Peter Stein.
In 2005, Robinson Savary directed his debut feature film, Bye Bye Blackbird, a dark fairy tale written by Arif Ali-Shah, featuring James Thiérrée, Jodhi May, Derek Jacobi, Izabella Miko and Michael Lonsdale.