Peake was born in Westhoughton, Bolton on 14 July 1974, the second of two daughters born to Glenys (née Hall) and Brian Peake. Her father was a lorry driver before working in the electrical industry, and her mother was a part-time careworker. Her older sister, Lisa, who was born in 1965, is a police officer. Peake’s parents separated when she was nine and she lived with her mother until the age of 15. When her mother moved in with a new boyfriend several miles away, Peake went to live with her grandfather so she could continue her [[|General Certificate of Secondary Education|GCSE]] studies at Westhoughton High School, before going on to take her A-Levels at Canon Slade School in Bradshaw. Her grandfather encouraged her to develop her creativity and start acting.

Peake portrayed Moors murderer Myra Hindley in See No Evil: The Moors Murders, which was broadcast in May 2006. In January 2009, Peake appeared in her first major feature film role, as Angela, in the film Clubbed.

In 2009, Peake left London after living there for 13 years. She said that living in Salford with her art director partner Pawlo Wintoniuk gave her the freedom to choose more risky roles and lower-paying jobs in theatre.

In 2012, Peake played the title role in Miss Julie at the Royal Exchange, Manchester, and previously played the part of Kristin in a 2000 production. She played Doll Tearsheet in the BBC2 adaptations of Henry IV, Parts I and II.

Peake wrote, directed and starred in the play Beryl: A Love Story On Two Wheels about the life of the Leeds-born cyclist Beryl Burton, which was broadcast on BBC Radio Four in November 2012. In 2014, Peake adapted her play for the stage. Titled simply Beryl, it was commissioned by the West Yorkshire Playhouse where it ran in June and July 2014 to coincide with the start of the Tour de France in Leeds. The play returned in June and July 2015 and toured across England in Autumn 2015. Peake wrote a later play called Queens of the Coal Age again for Radio 4 that told the story of Annie Scargill and three other women who tried to occupy a coal mine in 1993.

In September 2013, Peake was appointed an Associate Artist of the Royal Exchange Theatre in Manchester. Her association with the theatre began in childhood and she was a member of the youth theatre. Major productions in which she has performed include The Children’s Hour in 2008, for which she won a MEN Award, and Miss Julie in 2012 for which she won a Manchester Theatre Award. All of her performances at the Royal Exchange have been directed by Sarah Frankcom with whom she also collaborated on The Masque of Anarchy in 2012 for the Manchester International Festival. Building on this work, in September 2014 Frankcom went on to direct her as the title character in a radical re-imagining of Hamlet. The demand for tickets was so great that the production was extended for a week, having been “the theatre’s fastest-selling show in a decade”. The Guardian said of her performance: “Peake’s delicate ferocity, her particular mixture of concentration and lightness, ensure that you want to follow her whenever she appears”. A year later she appeared in Frankcom’s production of The Skriker, as “Caryl Churchill’s shape-shifting, doom-wreaking fairy”. The Guardian’s Lyn Gardner listed the production in her top ten British plays of the year. In 2016, Peake resumed her partnership with Royal Exchange Artistic Director, Sarah Frankcom, to star as Blanche Dubois in Tennessee Williams’ A Streetcar Named Desire. Peake’s performance in the role garnered critical acclaim with The Guardian describing her performance as “exquisite” and “breathtaking”.

Peake is a feminist and socialist. She was active in communist organisations during her youth and a member of the Communist Party of Britain. In January 2014, Peake won the first Bolton Socialist Club Outstanding Contribution to Socialism Award, for using her work to oppose the government’s “crippling austerity measures”.

Peake provided the vocals for the Eccentronic Research Council’s 2012 concept album 1612 Underture about the Pendle Witch Trials and for their 2015 album Johnny Rocket, Narcissist & Music Machine…I’m Your Biggest Fan. Peake also features as a crazed stalker in the music video for “Sweet Saturn Mine” by Moonlandingz; a collaborative effort by Eccentronic Research Council and Fat White Family in 2015.

In July 2015, Peake endorsed Jeremy Corbyn’s campaign in the Labour Party leadership election. She wrote on her website: “For me, Jeremy Corbyn is our only beacon of hope to get the Labour Party back on track, get the electorate back in touch with politics and save this country from the constant mindless bullying of the vulnerable and poor.”

In January 2016, Peake featured in the Climate Coalition’s short film I Wish For You as Mia, with Jeremy Irons starring as her grandfather, to highlight the urgency of combating climate change.

In 2016, along with other celebrities, Peake toured the UK to support Jeremy Corbyn’s bid to become Prime Minister.

In April 2017, Peake endorsed Labour Party leader Jeremy Corbyn in the 2017 UK general election. She said: “I am a Corbyn supporter. My mind boggles why people treat him like the anti-Christ, but it goes to show people are a lot more right-wing than they like to believe.”

Peake starred as the eponymous protagonist in the 2018 film Funny Cow alongside a cast including Paddy Considine and Stephen Graham. Tony Pitts wrote and starred in the film, which received positive reviews, in particular for Peake’s “magnificent” performance.

Peake starred in, and won critical acclaim for, the lead role of Winnie in Samuel Beckett’s Happy Days at the Royal Exchange Theatre in May 2018. The Guardian said she gave a “brilliant central performance, there’s barely a breath between optimism and despair”. Following Happy Days, the theatre presented Queens of the Coal Age, a play written by Peake. Adapted from her earlier radio drama, Queens of the Coal Age looks at the 1993 pit closure protests by miners’ wives in northern England. The play received mixed reviews.

Peake starred in The Nico Project as Velvet Underground singer Nico at the Manchester International Festival in July 2019.

In November 2019, along with other public figures, Peake signed a letter supporting Labour Party leader Jeremy Corbyn describing him as “a beacon of hope in the struggle against emergent far-right nationalism, xenophobia and racism in much of the democratic world” and endorsed him in the 2019 UK general election.

Peake stars as Miss Fozzard in the 2020 BBC remake of Alan Bennett’s Talking Heads, recreating a role originally played by Patricia Routledge.

In June 2020, she took part in an interview with The Independent, in which she stated that the practice of police officers in the United States kneeling on someone’s neck, one example of which led to the killing of George Floyd in Minneapolis, was “learnt from seminars taught by Israeli secret services”. The Independent amended the original article to add a note that “the allegation that US police were taught tactics of ‘neck kneeling’ by Israeli secret services is unfounded”. Peake later stated that she was “inaccurate in [her] assumption of American police training and its sources”. Peake initially claimed that the report was backed up by research from Amnesty International but had to backtrack from this after the organization publicly stated that while they had done critical research on the ties between worldwide police departments and Israeli authorities, they did not claim the actions described by Peake had ever happened.