Findlay was born and raised in Cookham, Berkshire. Her mother, Beverley, is a teacher's assistant and former nurse, and her father, Christopher Brown-Findlay, is a financial adviser and former investment banker. Her father's family is of Scottish descent, with roots in Glasgow; her great-grandfather, William Brown Findlay, incorporated his own middle name into his surname. Findlay trained with the National Youth Ballet and the Associates of the Royal Ballet. At age 15, she was invited to dance with the Kirov at the Royal Opera House for a summer season.
Findlay was cast in the lead role of Emelia in the film Albatross, directed by Niall MacCormick. She was subsequently cast in two episodes of the E4 programme Misfits and in Downton Abbey, she played the youngest daughter of the Grantham household for three seasons before subsequently leaving the show to move forward in her career. She appeared in the second episode of Channel 4's Black Mirror. In 2012, she became the face of Dominic Jones' jewellery line and was cast in Not Another Happy Ending by John McKay, and in the miniseries Labyrinth, based on the novel of the same name written by Kate Mosse, portraying Alaïs Pelletier. In 2012, she was cast as Beverly Penn in the film adaptation of the novel Winter's Tale (2014).