Wilson is a three-time Olivier Award nominee, and two-time winner, earning the Best Actress for the titular role in Anna Christie, and Best Supporting Actress for her portrayal of Stella Kowalski in A Streetcar named Desire. She has won a Golden Globe for her role in The Affair and received nominations for a British Academy Television Award for Best Actress and a Golden Globe Award for Best Actress – Television Series Drama for her role in Jane Eyre.
Wilson was born in Ashford, Surrey, the daughter of Mary, a probation officer, and Nigel Wilson, an investment banker. She has three older brothers Toby, Sam and Matthew and is the granddaughter of novelist and MI6 officer Alexander Wilson and his third wife, Alison (née McKelvie). She grew up in Shepperton, Surrey, and was raised Catholic.
Wilson attended Notre Dame School, an independent Catholic school for girls located in Cobham, before attending sixth form at Esher College. As a teenager, she worked as a model, and went on to study history at the University of Nottingham, graduating in 2003. While at Nottingham, she was also involved in student drama at the New Theatre. She graduated from the London Academy of Music and Dramatic Art (LAMDA) in July 2005. Afterwards, she co-founded Hush Productions. During her time at Nottingham, she participated in the TV war strategy game Time Commanders, helping her teammates fight in the Battle of Pharsalus.
Prior to her role in Jane Eyre, Wilson had one professional screen credit, in Suburban Shootout, a situation comedy she starred in with Tom Hiddleston.
In 2006–07, she filmed the second series of Suburban Shootout, a new Agatha Christie's Marple mystery (Nemesis) for ITV, and Stephen Poliakoff's BBC television drama Capturing Mary as the young Mary.
In 2007, Wilson appeared in Gorky's Philistines, playing Tanya, at the National from May until August. In June, she presented the 2007 Lilian Baylis Awards. Other projects in 2007 included a guest appearance in the sitcom Freezing as Alison Fennel (transmitted on BBC2, 21 February 2008); narration of the documentary The Polish Ambulance Murders (transmitted on BBC4, 5 February 2008); and the portrayal of a mentally ill doctor in the dramatised documentary The Doctor Who Hears Voices (transmitted on UK Channel 4, 21 April 2008).
From 23 July to 3 October 2009, she appeared as Stella in the Donmar revival of A Streetcar Named Desire. On 15 November 2009 AMC Television and ITV premiered the 2009 TV miniseries remake of The Prisoner, in which Wilson played the Village doctor, "Number 313." She played "Queenie" in an adaptation of Andrea Levy's Small Island, which aired on BBC1 in December 2009 and also aired in the United States on PBS in 2010.
From 2010 to 2013, she appeared in the British psychological police drama Luther as recurring character Alice Morgan, a research scientist and highly intelligent sociopath. In September 2012, the series' creator, Neil Cross, announced that he was in the process of creating a spin-off of Luther centred on Wilson's character. Cross stated, "The BBC is very interested in the project. The only real question would be how many and how often we would do it – whether it would be a one-off miniseries or a returning miniseries, a co-production or not."
From 4 August to 8 October 2011, Wilson starred in the title role of Eugene O'Neill's Anna Christie at the Donmar Warehouse alongside Jude Law. Her performance prompted The Guardian to devote an editorial to Wilson's "courageous, edgy and compelling talent".
In 2014, Wilson began starring as Alison Bailey on The Affair, for which she won the Golden Globe Award for Best Actress – Television Series Drama in January 2015. The show has now run for three seasons and was renewed for a fourth in January 2017.
Her film I Am the Pretty Thing That Lives in the House, directed by Oz Perkins, premiered at the 2016 Toronto International Film Festival.
From December 2016 to February 2017, Wilson starred in the title role of Hedda Gabler in a new version by Patrick Marber at the National Theatre. The play, and Wilson's performance in particular, received critical acclaim.