Carr was born in Slough, Berkshire to Irish parents and was educated at Burnham Grammar and later at the Royal Grammar School, High Wycombe where he achieved 4 A grades at A-level, before going on to receive a 2:1 degree in Social and Political Sciences from Gonville and Caius College, Cambridge. After leaving Cambridge, Carr was hired by the oil company Shell as a marketing executive, a job which he described as "the easiest job in the world". Less than two years afterwards, he took redundancy and joined JC Productions Ltd in order to begin a career in stand-up comedy.
