Walker was born in Stepney in the East End of London and has an older brother. She attended Saint Nicholas School, Old Harlow, and Forest School, Walthamstow, and undertook acting classes from age 12 in order to speak to boys. Interviewed in 2014 by The Guardian, she said, "I was really encouraged by my mother. My dad thought it was a ridiculous thing to do."
Walker was again nominated for a Television BAFTA for "Best Supporting Actress" in 2014 for her role in Last Tango in Halifax, but the award was won by her co-star Sarah Lancashire.
In 2014, she starred alongside Mark Strong and Phoebe Fox in Arthur Miller's play A View from the Bridge, at the Young Vic theatre. The play received extremely positive reviews from critics and transferred to Wyndham's Theatre in London's West End in 2015 and to the Lyceum Theatre on Broadway.