Allen was born in Hammersmith, west London, daughter of Keith Allen, a Welsh-born comedian, and film producer Alison Owen. She has an older sister, Sarah; a younger brother, actor Alfie (who was the subject of her song "Alfie"); and a younger sister, Rebecca. She is the goddaughter of Wild Colonials vocalist Angela McCluskey. She is the third-cousin of singer Sam Smith.

Allen began dating musician Ed Simons of the Chemical Brothers in September 2007, and in December, Allen announced that she and Simons were expecting a child. She suffered a miscarriage in January 2008. Following five months of dating, Allen's relationship with Simons ended soon after her miscarriage. Allen has stated that she spent three weeks in a psychiatric clinic due to depression following the miscarriage. Allen expanded on this in February 2017 explaining that she has also been diagnosed with bipolar disorder and Post traumatic stress disorder. In July 2009, Allen began dating Sam Cooper, a builder and decorator. On 5 August 2010, Allen announced that she was pregnant with her and Cooper's first child, later confirmed to be a boy due early in 2011. She experienced complications early in the pregnancy, including "about a week and a half of really heavy bleeding." In late October, six months into her pregnancy, Allen contracted a viral infection which caused her to suffer a stillbirth, announced on 1 November. On 6 November, Allen was admitted to a hospital, where she responded well to treatment for septicaemia. Allen and Cooper became engaged in December 2010 while on holiday in Bali. They wed on 11 June 2011 at St. James church in Cranham, Gloucestershire, England. The designer of Allen's wedding dress confirmed she was several months pregnant on the wedding day. Allen gave birth to a daughter in 2011. She gave birth to her second daughter in 2013. Allen has spoken publicly about her seven-year stalking ordeal and the effect it had on her life. Her stalker, Alex Gray, who had sent an email to his mother stating he was planning on murdering a celebrity, spent nights in her back garden, broke into her bedroom whilst she was sleeping and ultimately forced Allen to move. She has strongly criticised the Metropolitan Police for their inaction in the case, which included refusals to show Allen a picture of her stalker, lending her a panic alarm before demanding it back and refusal to believe stalking incidents were linked. Allen is a cricket fan and has appeared on Test Match Special.

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