Press' first credited screen role was in a 2001 episode of the BBC television series "Holby City". Her film debut and first lead role was in the short film "Wasp" (2003), which went on to win the Academy Award for best short film in 2005. She was recognised by the London Film Critics Circle and the Evening Standard British Film Awards for her work in "My Summer of Love" (2004) and nominated for a European Film Award in the category of Best European actress the same year. She made her professional stage debut in "The Weather", a new play Clare Pollard, performed as part of the Royal Court Theatre's 2004 Young Playwrights Season. In 2005, Press appeared as Caddy Turveydrop (née Jellyby) in the acclaimed BBC serialisation of Dickens' "Bleak House". Also in 2005 she appeared in the BBC television drama "Mr. Harvey Lights a Candle".