Burton-Hill's first job in journalism was as a staff writer at Vogue and she has since written for many major UK publications, including The Economist, The FT Weekend, The Guardian, The Observer, The Independent, The Sunday Times, The Sunday Telegraph, The Times Literary Supplement, Elle, and The Mail on Sunday. Her subjects range from the arts to artificial intelligence. She has been the music columnist for BBC Culture since 2013 and is BBC Music Magazine's chief interviewer. She was previously the UK's youngest broadsheet columnist, at The Daily Telegraph; a contributing editor for The Spectator; and a columnist at Total Politics and The Liberal magazines.
In January 2009, Burton-Hill's first novel, The Other Side of the Stars, was published by Headline Review, a division of Hodder Headline. She then signed a new two-book deal with Headline, and All The Things You Are was published in October 2013.
In October 2017, her first non-fiction book, Year of Wonder: Classical Music for Every Day was published, by Headline Home, also a division of Hodder Headline. The book has since been sold around the world, and the United States edition was published in November 2018 by Harper Wave, a division of HarperCollins. She also recorded the audiobook version.