Badham was born in Sydney. Her parents worked in the New South Wales gaming and track industry, with her father eventually working as a manager in the registered club industry. The influence of her upbringing was evident in work presented to her teachers at school; Badham's first script was a second grade assignment to write up the class Nativity Play, which she set in the beer garden of a public house with Mary and Joseph ejected by a manager for failing to meet dress regulations.
She studied creative writing and performance at the University of Wollongong, graduating with Bachelor of Arts and Bachelor of Creative Arts (Honours) degrees. At university, Badham won the Philip Larkin Poetry Prize in 1997, and the Des Davis Drama Prize and Comedy Prize in 2000. In 2001, she went on exchange to the University of Sheffield to study English literature.
While a student she began to publish poetry and short fiction as well as write student dramas. At university, she was drawn into involvement with student politics and left-wing activism, and she was elected editor of the Wollongong University Student Representative Council newspaper, Tertangala. She worked with the Student Union as Media Officer and Women's Officer, and sat on the Academic Senate and University Internationalisation Committee. By 1998, Badham was an avowed anarchist and Small and Regional Campuses Officer and then President of the New South Wales branch of the National Union of Students, caucusing with radical group Non Aligned Left. In 2013, she completed a Master of Arts degree with First Class Honours in Theatre at the Victorian College of the Arts, University of Melbourne.
In 1999, Badham won the Naked Theatre Company's first "Write Now!" play competition and with it a production of her winning play, The Wilderness of Mirrors, at the Sydney Theatre Company's Wharf studio. About secret service infiltration of an activist organisation, the play brought her to public attention and she began to stage more work across Australia. In 2001, she relocated to the United Kingdom.
In the UK, Badham's work was discovered by the Crucible Theatre, Sheffield, who staged a collaborative production of Kitchen with Nabokov Theatre in 2001. A play about marriage as a metaphor for capitalism, it then toured to the 2002 Edinburgh Festival Fringe, where it became a critical success. A 2003 play, Camarilla, was a critical success at the 2003 Edinburgh Festival Fringe, cementing Badham's international reputation as a proponent of radical political theatre. Badham was appointed Literary Manager of London's Finborough Theatre in 2009 and worked there until relocating to Melbourne to become an artistic associate at the Malthouse Theatre from 2011–2013. Badham's awards for her theatre work include the 2005 Queensland Premier's Literary Award for Black Hands / Dead Section, the 2014 New South Wales Premier's Literary Award for Muff and the 2014 Western Australian Premier's Book Awards for The Bull, the Moon and the Coronet of Stars.
In 2009 it was announced that Badham had been signed for a three-book deal by Pan Macmillan Australia. Her first book, Burnt Snow, was released in September 2010.
In 2013, Badham began publishing political commentary and arts criticism in Guardian Australia. Her commentary has also appeared in publications The Sydney Morning Herald, The Drum, The Hoopla, Women's Agenda, Australian Cosmopolitan and Daily Life. As a commentator, she has been a guest of Radio National, Sunrise and the Wheeler Centre and in 2014, 2015 and 2016 was a panellist on ABCTV's Q & A programme.