Berrington was born in Oxford, England. She has three siblings. Berrington attended Cheney Schol and studied Development Geography at London's Kings College. She later worked as an aide to Labor Party MP Siobhain McDonagh before auditioning at the Guildhall School of Music and Drama.
While at Guildhall, she made her stage debut in the lead role of Children's Children and appeared in Michael Winterbottom's film The Look of Love, also starring Stephen Fry. After graduating in 2012, Berrington starred as Jane Shore, one of Edward IV's mistresses, in the BBC2 miniseries The White Queen, opposite James Frain. Berrington also appeared in the comedy series Outnumbered and starred in the thriller The Last Showing. In 2015, she appeared in AMC's Humans as well as the History Channel miniseries Sons of Liberty (with Dean Norris).