Kingston was born and brought up in Epsom, Surrey, the eldest of three daughters of an English butcher, Anthony Kingston, and his German wife, Margarethe (née Renneisen). Kingston's paternal great-great-grandmother was Jewish, an ancestry Kingston explored on the series Who Do You Think You Are? Kingston's uncle, her mother's younger brother, is actor Walter Renneisen. Her sisters are Susie, who is mentally and physically disabled as a result of being deprived of oxygen at birth, and Nicola, a former actress who appeared in the 1996 British TV production of The Fortunes and Misfortunes of Moll Flanders, in which Kingston starred.
Kingston was inspired to pursue acting by one of her teachers at Rosebery School for Girls. Kingston auditioned and performed in the Surrey County Youth Theatre production of Tom Jones as Mrs Fitzpatrick, alongside Sean Pertwee as Captain Fitzpatrick and Thwackum played by Tom Davison. She later completed a three-year programme at the Royal Academy of Dramatic Art and went on to join the Royal Shakespeare Company.
Kingston has appeared in a number of British-produced television dramas, including Grange Hill, Crocodile Shoes, The Fortunes and Misfortunes of Moll Flanders, The Knock and various guest roles on The Bill.
Kingston's film credits include The Cook, the Thief, His Wife & Her Lover (1989), A Pin for the Butterfly (1994), The Infiltrator (1995), Croupier (1998), Essex Boys (2000), Boudica (Warrior Queen in the USA) (2003) in which she played the eponymous Boudica, Sweet Land (2005) and Crashing (2007).
In September 1997, Kingston gained North American television fame after being cast on the long-running medical drama ER. Her first appearance was in the premiere of the fourth season, the award-winning live episode "Ambush", as British surgeon Elizabeth Corday. Kingston played this role for just over seven seasons, leaving in October 2004 with the season 11 episode, "Fear". In spring 2009, Kingston returned to ER during its 15th and final season for two episodes, "Dream Runner" and the two-hour series finale, "And in the End...".
In November 2005, Kingston guest-starred in the long-running mystery drama Without a Trace in the season 4 episode, "Viuda Negra". The episode was directed by Kingston's former ER castmate Paul McCrane. She played Lucy Costin, a wealthy vacationer from the U.S. whose husband is kidnapped by a Mexican street gang during their honeymoon.
In 2006, Kingston starred as Nurse Ratched, opposite Christian Slater as Randle Patrick McMurphy, in the Garrick Theatre's West End production of One Flew Over the Cuckoo's Nest. Kingston revealed that she auditioned for role of Lynette Scavo on ABC's Desperate Housewives, but was turned away for being too curvy.In a 2006 interview, she admitted to considering and nearly attempting suicide after her separation from her husband Ralph Fiennes.
In 2008, Kingston guest-starred in the fourth series of the long-running science fiction television programme Doctor Who in the two-part story "Silence in the Library"/"Forest of the Dead" as River Song. She reprised the role in fifteen episodes in 2010, 2011, 2012, 2013 and 2015. Kingston says she thought her role was simply a one-off, but was delighted that she would be a returning character. Kingston returned as the character in the 2015 Christmas special, "The Husbands of River Song". It was her first appearance alongside Peter Capaldi's Twelfth Doctor.
In September 2008, Kingston took the part of Mrs. Bennet in ITV's acclaimed four-part production Lost in Austen which is based on Jane Austen's Pride and Prejudice. In October that same year, Kingston appeared in the police procedural drama CSI: Crime Scene Investigation in the season 9 episode, "Art Imitates Life" as Patricia Alwick, a psychiatrist and grief counsellor who helps the team cope with the recent death of CSI member Warrick Brown.
In February 2009, Kingston portrayed Miranda Pond, a defence attorney in two episodes of the legal drama Law & Order: Special Victims Unit. This guest spot reunited Kingston with her former castmate from ER, Mariska Hargitay. In June, Kingston starred as the lead character Ellie Lagden, one of four former convicts in the BBC One drama series Hope Springs until its cancellation in July. In September that year, she had a recurring role in FlashForward, playing Inspector Fiona Banks.
In 2010, Kingston returned to Law & Order: Special Victims Unit in the season 12 episode, "Trophy", which reunited Kingston with her former ER castmate Maria Bello.
In 2011, Kingston was a cast member on British supernatural series Marchlands, portraying Helen Maynard. She also guest-starred in the Grey's Anatomy spin-off Private Practice as Marla Tompkins, a psychiatrist who writes book reviews for newspapers. Kingston appeared in Friedrich Schiller's Luise Miller at the Donmar Warehouse in London.
In early 2013, Kingston appeared in Arrow, playing Professor Dinah Lance, the mother of Laurel and Sara Lance.
In July 2013 Kingston played Lady Macbeth opposite Kenneth Branagh in Macbeth at Manchester International Festival. Her performance was broadcast to cinemas on 20 July as part of National Theatre Live. She reprised the performance with Branagh at the Park Avenue Armory in June 2014. It was her New York stage debut.
In September 2014, Kingston starred as Ruth Hattersley, an analyst working for the Missing Persons Bureau on the ITV mini-series drama Chasing Shadows.
Kingston met English actor Ralph Fiennes while they were both students at the Royal Academy of Dramatic Art. They were together for ten years before marrying in 1993. In 1995, Fiennes began an affair with his Hamlet co-star, Francesca Annis, and left Kingston the following year; they were divorced in 1997.
At the end of 1998, Kingston married her second husband, German writer and freelance journalist Florian Haertel, having met the previous year on a blind date arranged by friends; they have a daughter together, Salome Violetta Haertel, born 28 March 2001. Kingston and Haertel separated in 2010. Kingston married television producer Jonathan Stamp in a ceremony in Rome on 18 July 2015.
As of 2011, Kingston continues to reside in the United States.
Kingston appeared on the BBC genealogy series Who Do You Think You Are? in September 2012, investigating the lives of her great-grandfather Will Keevil and her four-times great-grandmother, Elizabeth Braham.