Eve was born in London, England, the daughter of actors Trevor Eve and Sharon Maughan. She has two younger brothers, Jack and George, and was raised in the United Kingdom and Los Angeles, United States. She attended Bedales and then did her A-Levels at Westminster School in London. During her gap year, she studied at the Beverly Hills Playhouse and then English at St Catherine's College, Oxford. While at Oxford she appeared in student productions of An Ideal Husband, Animal Crackers, Scenes from an Execution and The Colour of Justice.
Eve lives in London and New Jersey . She has dated Ben Adams and Rafe Spall whom she met while working on The Rotters Club. She was once named sixth most eligible woman in Britain by Tatler magazine. In 2001 she dated Phil Lin from Rancid. In April 2009 she started dating a poet, Adam O'Riordan, whom she met when they were both undergraduates at Oxford. She also has two different color eyes (heterochromia), one blue and one green.