[4] Skinner's play Eigengrau, staged at the Bush Theatre in 2010, was a critical and box office hit and Skinner was nominated for the Evening Standard Award for Most Promising Playwright in 2010.

Her play The Village Bike was her first play to be staged at the Royal Court Theatre where it had a sell out, twice-extended run starring Romola Garai and directed by Joe Hill-Gibbins, winning her the George Devine Award and the Evening Standard Award for Most Promising Playwright in 2011.

In the same year, her play The Sound of Heavy Rain was produced by Paines Plough and Sheffield Theatres touring in Roundabout.

[6] In 2015, Skinner's play "Linda", staged at London's Royal Court theatre, "raises important questions with bracing rhetorical force" Timeout.

Also in 2015, her off-broadway play "The Ruins of Civilisations" was described as offering "a powerful portrait of an anguished woman fixating on the prospect of a baby as a source of affection, hope and escape" by The Guardian, In 2018, her play "Meek", staged at the Traverse in Edinburgh, "probes into power, resistance and men's rights"[7][8][9] In 2023, Skinner's play "Lyonesse" opened at The Harold Pinter Theatre.