Conn was born in Barnet, London, England. "A self-described army brat, Conn was born in London and lived overseas in Germany and Gibraltar with her parents and two older sisters. Her family settled in the London suburbs. She acted in school plays and did a post-grad drama program in London." She is the great niece of actress Merle Oberon (Oberon's brother was Conn's grandfather).
After drama school, Conn had a series of bit-parts in various British films, before coming to prominence in Series Five of the popular BBC One series Down to Earth. In 2001, she picked up the role of PC Miriam Da Silva in BBC1's Mersey Beat and an irregularly recurring role in Casualty.
Conn has now developed her roles between all three media (television, film and theatre), with a series of leading roles in various small budget European as well as British films; BBC character dramas such as The Innocence Project; and occasional returns to the RSC.