After drama school, Conn had a series of small roles in various British films, before coming to prominence when she starred as Ashika Chandiramani in the BBC series Party Animals. In 2001, she picked up the role of PC Miriam Da Silva in BBC1's Mersey Beat and an irregularly recurring role in Casualty. The following year, Conn made her West End theatre stage debut in three plays after transferring from Stratford-upon-Avon in the Royal Shakespeare Company's Jacobean Season at the Gielgud Theatre – The Island Princess, Eastward Ho! and The Roman Actor.
Conn has appeared television, film and theatre, with a series of leading roles in various small budget European as well as British films namely BBC character dramas such as The Innocence Project, and occasional returns to the RSC. Conn joined Series Five of the popular BBC One series Down to Earth in 2004. In early 2008, she starred as Miranda Hill in The Palace, as Jessica in Mistresses and as Neela Sahjani in Trial & Retribution. That same year, Conn appeared as Claire in Dead Set. In 2010, she played Danni Prendiville in the TV series Strike Back.
Conn was chosen by Steven Spielberg to be one of the leads in the $150million TV series Terra Nova, which premiered on 26 September 2011.[3] In 2014, she appeared in a US TV series called The Lottery.[4]