Huston was born in London, England. Her mother was the American ballerina Enrica "Ricki" Soma and her biological father is John Julius Norwich (Viscount Norwich). When Huston was four, her mother died in an automobile accident and she was subsequently brought up by film-maker John Huston (1906—87), her mother's estranged husband (Soma was his fourth wife). Allegra Huston's maternal half-siblings include actress Anjelica Huston and writer and falconer Tony (Walter Anthony) Huston. Their half brother actor Danny Huston is her step brother. Her paternal half-siblings are writer Artemis Cooper and architect and singer Jason Cooper. She played a small role in her brother Danny's film Mr. North.

After gaining a First Class degree in English Language and Literature from Hertford College, Oxford, Huston worked in book publishing in London, first at Chatto & Windus and then at Weidenfeld & Nicolson, where she was Editorial Director from 1990 to 1994. After two years as Acquisition and Development Consultant at Pathe Films, London, she left to write and edit freelance. Her articles have appeared in The Times, The Tatler, The Independent on Sunday, French and US Vogue, Mothering, People, and Harper's Bazaar (UK). Since 2004 she has been co-director of The Imaginative Storm writing workshops with poet James Nave (www.imaginativestorm.com).She resides in Taos, New Mexico, along with her partner Cisco Guevara, noted storyteller and president of Los Rios River Runners, New Mexico's oldest and largest rafting company, and their son Rafael.

Huston is the author of Love Child: A Memoir of Family Lost and Found published in April 2009 by Simon & Schuster (US) and Bloomsbury (UK).