Carr co-hosted the BBC's Royal Television Society award-winning Ouch! Podcast with Mat Fraser from 2006 to 2013, and in 2011 worked as a researcher for the BBC comedy panel show Have I Got News for You.
In 2007 she was Runner up in the Hackney Empire New Act of the Year competition.
For the past 20 years, Carr has been a disability rights campaigner in the UK and has spoken at many rallies. In May 2008 she joined with ADAPT, a prominent disability rights group in the United States, to raise money for ADAPT and to protest against presidential candidate John McCain's refusal to support the right of people with disabilities to live in their own homes.
Carr was born in Port Sunlight and grew up in Bebington. She attended Upton Hall School FCJ in Upton, Merseyside. and Birkenhead High School in Birkenhead. In 2010 Carr entered into a civil partnership with longtime partner Jo Church in what Carr called "A Wheelie Special Wedding". Her father gave a speech in which he was prohibited from using words like "brave". Carr and her partner danced to the Dirty Dancing theme and the local fire brigade held her, and her chair, aloft.
In 2011, Carr was part of a Newsnight debate on assisted suicide, following the screening on the BBC of Terry Pratchett: Choosing to Die, which included Jeremy Paxman and David Aaronovitch.
Carr was in her thirties when she took on her first professional acting role playing Mother Courage before heading to the Young Vic with another Bertolt Brecht play, The Exception and the Rule. In 2013, she joined the long-running BBC crime thriller series Silent Witness as regular character Clarissa Mullery.
On 10 August 2017, Carr and her personal assistant were the victims of an attack by a man armed with scissors. The assailant was subsequently arrested and detained under the Mental Health Act.
She opposes Lord Faulkner's Assisted Dying Bill, stating: "I fear we’ve so devalued certain groups of people – ill people, disabled people, older people – that I don’t think it’s in their best interests to enshrine in law the right of doctors to kill certain people."
