Born Simone Ashwini Pillai to Indian Tamil speaking parents Latha and Gunasekharan Pillai, Ashley is from Camberley, Surrey, and has an older brother, Sean Pillai. Ashley has spoken about how despite growing up in a household of academics, she was always drawn more towards the creative fields. Her parents were hesitant about her inclination to the arts. "My parents were quite protective over me", she told Glamour. "They're first generation. They came from India to this country, so they didn't really have a life where they could choose to be whatever they wanted." Ashley grew up singing classical music, opera, and playing the piano.
Ashley's family later moved to Beaconsfield, where she attended Beaconsfield High School and then Redroofs Theatre School in Maidenhead for sixth form. She left school early at sixteen, describing herself as "very stubborn" and "wishing my life away". She spent some of her teen years in Ojai, California, where she has relatives. She signed with a modelling agency and began auditioning when she was 18. She then studied acting at Arts Educational Schools (ArtsEd) in West London.