Zinovieff was born in London. She is of Russian descent on her father's side, her grandparents having left St Petersburg for the United Kingdom shortly after the 1917 revolution. She grew up in Putney in south-west London with her mother, a psychotherapist, and her father Peter Zinovieff, founder of Britain's first synthesizer manufacturer, Electronic Music Studios Ltd. She attended Cambridge University and later gained a PhD.
Zinovieff has worked as a journalist and book reviewer for various British publications, and is the author of "Eurydice Street: A Place in Athens" and "Red Princess: A Revolutionary Life," both published by Granta. "Eurydice Street" is an account of her first year living in Athens and "Red Princess" is a biography of her Russian grandmother.
Eurydice Street: A Place in Athens (2004). ISBN 1862077509 ISBN 978-1862077508
Red Princess: A Revolutionary Life (2007). ISBN 1862079196 ISBN 978-1862079199 - A book on the life of her grandmother - Sofka Dolgorouky