Martin was born in Beverley, near Hull, England in May 1978 and attended Beverley High School where she appeared in school plays. She adopted the middle name Maxwell (her grandfather's name) to distinguish her from another member with the same name when she joined Equity. Her father was the managing director of a pharmaceutical company and her mother was a research scientist. Her mother gave up her job to bring up Anna and her elder brother Adam. After she left school Martin studied history at Liverpool University, specialising in the First World War. She joined the London Academy of Music and Dramatic Art (LAMDA) after completing her studies at Liverpool. In her final year at LAMDA her father was diagnosed with cancer, although he lived long enough to see her stage performance as Alexandra in The Little Foxes at the Donmar Warehouse (he died when she was 24).

Martin's partner is director Roger Michell; she gave birth to their first child, Maggie, in April 2009.

Martin first came to prominence on the London West End stage playing the leading role of Lyra in the National Theatre's production of Philip Pullman's His Dark Materials. She was then cast in the part of Bessie Higgins in the BBC television adaptation of the Elizabeth Gaskell novel, North and South, in 2004, and made a guest appearance in the 2005 series of Doctor Who. She played Esther Summerson, the central character in the 2005 BBC adaptation of Charles Dickens' Bleak House, for which she won the Best Actress BAFTA Television Award in 2006.

In January 2006 she took part in a reading of The Entertainer at the Royal Court Theatre, and in February and March she appeared in Laura Wade's Other Hands, directed by Bijan Sheibani at the Soho Theatre. She is the narrator of the CD version of The Foreshadowing, a children's book about the First World War by Marcus Sedgwick, which was published in May 2006.

In the same year she worked on I Really Hate My Job, directed by Oliver Parker and, from October 2006 to April 2007, played Sally Bowles in Bill Kenwright and Rufus Norris's West End production of Cabaret at the Lyric Theatre.

She played Cassandra Austen in Becoming Jane, a 2007 film about the early life of the novelist Jane Austen starring American actress Anne Hathaway in the title role. At the end of the year she played the gaoler's daughter in Lee Hall's adaptation of The Wind in the Willows, a multi-million pound production by Box TV for BBC One, and was the joint narrator (with Anton Lesser) of the CD version of Tamar, a children's book about the Second World War by Mal Peet, which was published in December 2007.

In 2008 she starred in the BBC Two drama White Girl and with Naomie Harris in Channel 4's adaptation of Poppy Shakespeare, for which she won her second Best Actress BAFTA Television Award in 2009. From July to October of that year, she appeared with Dame Eileen Atkins in The Female of the Species at the Vaudeville Theatre in London. She also appeared in a BBC Radio 4 adaptation of Agatha Christie's novel Crooked House.

In July 2009 she appeared in the BBC Two drama, Freefall, and played Neil Armstrong's wife, Janet, in Moonshot: The Flight of Apollo 11, an ITV1 drama documentary to celebrate the 40th anniversary of the Apollo 11 moon landing.

In February 2010 she played freedom of information campaigner Heather Brooke in On Expenses, a BBC Four satirical drama and also played Isabella in Shakespeare's Measure For Measure at the Almeida Theatre.

In December 2010 she will play Sarah Burton in a three-part BBC adaptation of Winifred Holtby's novel, South Riding.