Duff was born in London on 8 October 1970, the younger of two children of Irish immigrants: her father was a painter and decorator from County Meath and her mother was from County Donegal and worked in a shoe shop. The family lived in Southall, London, and Anne-Marie went to Mellow Lane School. At an early age, Anne-Marie attended a local youth theatre, Young Argosy, linked to the Argosy Players, in order to battle her shy nature; she soon became hooked on the stage. In her mid-teens, involved in an amateur theatre company, she began to think seriously about applying to drama schools. Her first application was rejected. "At the time, I was desperately unhappy about it, but I just wasn’t polished. I got too nervous in the audition. It wasn't a world I was familiar with..." After further study of Film and Theatre, at the age of 19, she attended the Drama Centre in London, alongside John Simm, Anastasia Hille and her good friend, Paul Bettany.
Duff made her first television appearance in ITV drama Trial & Retribution as Cathy Gillingham for two episodes in 1997. She later made appearances in series such as Amongst Women, in Aristocrats as Lady Louisa Lennox and in 2003 BBC television film as Henrietta of England. She also had a minor role in Holby City as Alison McCarthy. Duff played Holly in the first series of Simon Nyesitcom, Wild West, alongside Dawn French and Catherine Tate in 2002. In 2002, Duff appeared in her first major film role as Margaret McGuire in The Magdalene Sisters. Duff’s first critical acclaim came as Fiona Gallagher in the Channel 4 television programmeShameless, and for her portrayal of Queen Elizabeth I in the lavish 2005 BBC television miniseries, The Virgin Queen which also starred Tom Hardy, Emilia Fox and Sienna Guillory. Duff returned to her role as Fiona for the final episode of Shameless in 2013. For Duff’s roles as both Fiona and Elizabeth I, she was nominated for the British Academy Television Award for Best Actress in both 2006 and 2007. She won the Broadcasting Press Guild award for Best Actress for her role as Fiona. , alongside Shameless co-star and then-husband James McAvoy in 2007 Following her breakthrough, Duff ventured into films, first appearing in Notes on a Scandal, alongside Judi Dench. After film roles in Irish film Garage and The Waiting Room, she next appeared in a main role in comedy filmFrench Film and Is Anybody There? in 2008. In 2009, Duff received further attention when she played the mother of John Lennon, Julia Stanley, a role for which she won British Independent Film Award for Best Supporting Actress in Nowhere Boy. She also appeared inThe Last Station, a biopic about Leo Tolstoy’s later years, she played his devoted daughter Sasha. She appeared in less known film roles following this before her appearance in 2014 filmBefore I Go to Sleep. Throughout this time, Duff continued to appear on mainstream television in Parade’s End, a five-part BBC/HBO/VRT television serial adapted from the tetralogy of eponymous novels by Ford Madox Ford as Edith Duchemin and in BBC Onecrime dramaFrom Darkness which premiered in October 2015, appearing in the starring role. Of Duff’s performance, Metro stated "Not a fan of police procedural dramas? Good, because this ain’t that. From Darkness is a character-driven tale of one women’s journey and resolve and it includes a bloody brilliant performance by Duff." In 2015, she played Violet Miller in the film Suffragette a working-class woman who introduces Maud Watts to the fight for women's rights in east London. "Violet is extraordinary, she's a firebrand - a tornado that comes into Maud's life and changes it forever. I found her thrilling," says Duff. In 2016, Duff was cast in a new BBC animated miniseries of Watership Down, alongside her former husband James McAvoy. It premiered in December 2018; Duff appeared as Hyzenthlay. In 2019, Duff once again appeared with McAvoy in the BBC One and HBO adaption of Philip Pullman’s His Dark Materials. In 2020, Duff portrayed Erin Wiley, the estranged heroin addict mother of established character Maeve in the second season of critically-acclaimed Netflix original seriesSex Education. In June 2020, Duff appeared in a main role as Tracy Daszkiewicz in three-part drama The Salisbury Poisonings. The series portrays the 2018 Novichok poisoning crisis in Salisbury, England, and the subsequent Amesbury poisonings. Duff narrated the BBC Two documentary Hospital in 2017. The series followed the NHS in unprecedented times.
An accomplished theatre actor, she has worked extensively with the Royal National Theatre, including its 1996 production of Helen Edmundson's adaptation of Leo Tolstoy's War and Peace, and also in London's West End. Credits at the National Theatre include Collected Stories, King Lear and the title character in Marianne Elliott's production of George Bernard Shaw's Saint Joan to great acclaim. In 2011 she played Alma Rattenbury in Rattigan's final play Cause Célèbre at The Old Vic directed by Thea Sharrock. Duff was nominated for a Laurence Olivier Award in 2000.
Duff married Scottish actor and former Shameless co-star James McAvoy in 2006, and gave birth to their son, Brendan McAvoy, in 2010. On 13 May 2016, Duff and McAvoy announced they were getting a divorce.
In 2007 she was one of nine female celebrities to take part in the What's it going to take? campaign promoting awareness of domestic abuse in the United Kingdom.