Tennant is of Scottish extraction, the daughter of Christopher Grey Tennant, 2nd Baron Glenconner, and Elizabeth Lady Glenconner. Born in London, she was educated at St Paul's Girls' School and spent the World War II years and her childhood summers at the family’s faux Gothic mansion in Peeblesshire. Her family also owned estates in Trinidad. Tennant’s remembers her father as a mix of rage and benevolence, and these memories may have influenced her fiction.
Tennant grew up in the modish London of the 1950s and 1960s. She worked as a travel writer for Queen magazine and an editor for Vogue. In the 1970s she edited a literary magazine, Bananas, which helped launch the careers of several young novelists. Tennant published her first novel, The Colour of Rain, under a pseudonym when she was twenty-six.
A large number of other books followed in a wide variety of genres: thrillers, children’s books, fantasies, and several revisionist takes on classic novels, including a "sequel" to Pride and Prejudice called Pemberley. In later years she began to treat her own life in such books as Girlitude and Burnt Diaries (both published in 1999). The French Dancer's Bastard, a fictional spinoff of Jane Eyre, was published in October 2006. The Autobiography of the Queen, written with Hilary Bailey, was published in October 2007.
Tennant has been married four times. One of her husbands was writer and political pundit Alexander Cockburn. She has two daughters and a son - author Matthew Yorke. In April 2008 she married her partner of 33 years, Tim Owens, saying it is for tax reasons.