Pugh made her US TV debut in the film "Studio City" (2015). She then starred in the independent drama "Lady Macbeth" and had a recurring role as a webcam model in the first season of the ITV detective series "Marcella".
In 2018, Pugh appeared in the action film "The Commuter" and played 'Cordelia' in Richard Eyre's television film "King Lear". She then played 'Elizabeth de Burgh' in the Netflix historical film "Outlaw King" (2018).
She next appeared in a six-part miniseries adaptation of author John le Carré's spy novel "The Little Drummer Girl".
She then starred as professional wrestler 'Paige' in "Fighting with My Family", played the lead role in Ari Aster's horror film "Midsommar", played 'Amy March', in Greta Gerwig's film adaptation of Louisa May Alcott