Ashton attended the Anna Scher Theatre, after school junior classes, and later became a member of the Anna Scher YPs (Young Professionals). As a teenager, in the late 1990s she starred in a BBC2 science show Science in Action as one of the three curious children.

Ashton began entering poetry slams at the age of seventeen, and won the London Poetry Slam Championship in 2000. In 2006 she was Young Writer in Residence at the Contact Theatre in Manchester. Her first play, Harm's Way, was shortlisted for the Verity Bargate Award in 2007, and premiered at the Lowry, Salford in 2008 as part of the National Youth Theatre’s new writing season. Her other plays have included Skunk, performed by the National Youth Theatre and Soho Theatre; and She from the Sea, performed in 2010 at the London International Festival of Theatre (LIFT). Ashton was co-writer of Suddenlossofdignity.com, Bush Futures Programme. One of her plays, For all Those Women who Thought they were Mad, was selected to be part of the Royal Court Playwriting Festival in 2009. Ashton contributed to the writing of The Children's Monologues, adapted from over 300 original stories by Tswana, Zulu and Sesotho children in South Africa and presented by Dramatic Need in 2010. She has worked with the Bush Theatre and the Clean Break theatre company.

In 2009, she appeared in St. Trinian's II: The Legend of Fritton's Gold. She was named as one of Screen International's Stars of Tomorrow 2009. Two years later she appeared alongside Jason Statham in the film Blitz and with Jason Isaacs in the television adaptation of Kate Atkinson's Case Histories. In 2011, Ashton starred in the BBC Christmas show Lapland. She also starred as Joyce Carol Vincent in the film Dreams of a Life in the same year, for which she was nominated in the Most Promising Newcomer category at the 2012 British Independent Film Awards.

Ashton was named in May 2010 as one of the "55 faces of the future" by Nylon magazine's Young Hollywood Issue. In October 2012, she was awarded the "Ultimate Newcomer" trophy by Cosmopolitan magazine at their Women of the Year awards. In November 2012 Ashton picked up the Creative Diversity Network Award for Best Breakthrough On-Screen Talent for her role as Vod in the BAFTA-nominated Channel 4 hit Fresh Meat. In 2013 Ashton won a Screen Nation Award for Female Performance in a Film 2012/2013, in recognition of her lead role performance in Dreams of a Life.

Her television work includes Holby City, The Bill, NCS: Manhunt, Casualty, The Crust, and Misfits. In 2011, Ashton starred in the Channel 4 comedy Fresh Meat, playing the part of Vod.

Ashton narrated thirteen episodes of 24 Hours in Police Custody, shown on Channel 4 in 2016 and 2017. She narrated a documentary Public Enemies: Jay-Z vs Kanye for the same channel in 2017.

In 2017, Ashton presented the third series of Random Acts, Channel 4's short film showcase in association with Arts Council England. Episode 2 included a film directed by Ashton, in which she took the lead role.