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 UK and Los Angeles. Eve 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 read English at St Catherine’s College, Oxford. While at Oxford she appeared in student productions of An Ideal Husband, Animal Crackers (which toured to the Edinburgh Fringe Festival), Scenes from an Execution and The Colour of Justice.