Birch grew up in South East London. She is of British, Italian and Irish descent. She trained at the Italia Conti Academy of Theatre Arts from 1987 to 1997, graduating with a Diploma in Performing Arts, and also studied Shakespeare at RADA and Drama at Yale University. She has one brother, who is four years her senior. Her great-aunt was one of the Gaiety Girls.
Birch played the role of Teresa di Marco in the BBC One soap opera EastEnders between 1998 and 2000. Her other television credits include One Night of Shakespeare, The Bill, Thief Takers and Renford Rejects. She also appeared in the pilot episode of the NBC Universal series Day One.
Birch's stage work includes plays at the award-winning Arcola Theatre, outdoor Shakespeare festivals, national tours and pantomime. In 2007 she acted with 'Shakespeare in the Valley', New Hampshire's only professional outdoor repertory Shakespeare festival. She also appeared in the world premiere of Twelfth Night: The Musical in London.
Leila was a guest host on episode 18 of the Retro Rejects podcast.
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