Chancellor was born in Richmond, London, England, the daughter of the Hon. Mary Alice Jolliffe (daughter of William Jolliffe, 4th Baron Hylton) and John Paget Chancellor. Through her mother's mother, Lady Perdita Rose Mary Asquith, Chancellor is the great-granddaughter of Raymond Asquith and the great-great-granddaughter of Prime Minister H. H. Asquith,[1] and through her father, she is the great-great-granddaughter of the 12th Earl of Winchilsea and Nottingham (a descendant of Thomas Cecil, 1st Earl of Exeter and William Cecil, 1st Baron Burghley). She is a second cousin, once removed of actress Helena Bonham Carter, through her mother's side. Her uncle is journalist Alexander Chancellor, the father of model Cecilia Chancellor, her eight-times great-aunt was author Jane Austen, herself a great-niece of James Brydges, 1st Duke of Chandos, and her second cousin six times removed was poet Lord Byron. She is also twice a descendant of Mary Boleyn and once of Richard Rich, 1st Baron Rich and John Churchill, 1st Duke of Marlborough.

Chancellor was accepted into the London Academy of Music and Dramatic Art, but in her third year she became pregnant and dropped out.[citation needed] Her daughter with Scots poet Jock Scott, Poppy Chancellor, was born in 1988. When their relationship ended, she then married a cameraman, Nigel Willoughby, whom she had met in 1993 while shooting a Boddington's advertisement. However, they divorced in 1998.[citation needed] She is now married to Redha Debbah.