She is so in-demand we had only been seated for five minutes when a waitress arrived with an invitation from a group of men at a nearby table for Alice to go to their party that night. She politely turned them down.
She will soon be seen in The Raven, a fictionalised account of the last days of Edgar Allan Poe in which he tracks a serial killer who has kidnapped Alice's character. Filmed in Serbia it was, she says, "a tough, gruelling shoot. I went through everything my character did, including being buried alive."
Then May sees the release of Men In Black III in which she plays Young Agent Oh, the 60s version of Emma Thompson's Agent Oh.
And she is currently filming the new, as-yet-untitled---and very secret --Star Trek movie at Sony Studios. "I'm not allowed to say anything about it at all, but it's such fun and we're all having an amazing time,." she says.