Her first play Come Out Eli won a Time Out Award. The Girlfriend Experience premiered at the Royal Court and then transferred to the Young Vic in 2009. Do We Look Like Refugees? won a Fringe First Award at the 2010 Edinburgh Festival. London Road opened at the National Theatre-Cottesloe in 2011 to widespread acclaim. It was named Best Musical at the Critics' Circle Awards and transferred to the National's larger Olivier stage in 2012. Her newest play Have I Been All My Life? opened at the New Vic Theatre in April 2012.
In other work, Blythe took part in Headlong Theatre's production of Decade at St Katherine's Docks. She wrote and co-directed a BBC2 documentary on the London riots. She is also working on a film script.