She was the daughter of Punch editor Edmund Knox and the niece of theologian and crime writer Ronald Knox, cryptographer Dilly Knox and Bible scholar Wilfred Knox. "When I was young," Fitzgerald later wrote,
I took my father and my three uncles for granted, and it never occurred to me that everyone else wasn't like them. Later on, I found that this was a mistake, but I've never quite managed to adapt myself to it. I suppose they were unusual, but I still think that they were right, and insofar as the world disagrees with them, I disagree with the world. 
She was educated at Wycombe Abbey and Somerville College, Oxford; she worked for the BBC during World War II. In 1941, she married Desmond Fitzgerald, an Irish soldier; they had three children, a son and two daughters. In the 1960s, she taught at the Italia Conti Academy, a drama school; she also worked in a bookshop in Southwold, Suffolk. For a time she lived in Battersea on the Thames, on a houseboat that reportedly sank twice.
She launched her literary career in 1975, at the age of 58, when she published a biography of Pre-Raphaelite artist Edward Burne-Jones (1833-1898). This was followed two years later by The Knox Brothers, a joint biography of her father and uncles in which she managed to never mention herself by name.
Later in 1977, she published her first novel, The Golden Child, a comic murder mystery with a museum setting inspired by the Tutankhamun mania earlier in the decade. The novel is said to have been written to amuse her terminally-ill husband, who died in 1976.
Over the next five years she published four novels, each connected in some way with her life experience. The Bookshop (1978), which was shortlisted for the prestigious Booker Prize, concerned a struggling bookstore in the fictional East Anglian town of Hardborough; set in 1959, the novel includes as a pivotal event the shop's decision to stock Lolita.
Fitzgerald won the Booker Prize with 1979's Offshore, a novel that takes place among Battersea houseboat community in 1961. Human Voices is a fictionalized account of wartime life at the BBC, while At Freddie's depicts life at a drama school.
At that point, Fitzgerald has said, she "had finished writing about the things in my own life, which I wanted to write about."  After writing a biography of the poet Charlotte Mew (1869-1928), she began a series of novels with a variety of historic settings.
First was Innocence (1986), in Italy in the 1950s, the story of a romance between the daughter of an impoverished aristocrat and a doctor from a southern Communist family. The Italian Marxist theorist Antonio Gramsci (1891-1937) appears as a minor character.
The Beginning of Spring (1988) takes place in Moscow in 1913, examining the world just before the Russian Revolution through the family and work troubles of a British small businessman who was born and raised in Russia.
The Gate of Angels (1990), about a young Cambridge University physicist who falls in love with a nurse after a bicycle accident, is set in 1912, a time when physics is about to enter a similarly revolutionary period.
Fitzgerald's final novel, The Blue Flower, published in 1995, centres on the 18th century German poet and philosopher Novalis, and his love for what is portrayed as a rather ordinary child. Other historical figures, like the poet Goethe and philosopher Karl Wilhelm Friedrich von Schlegel, feature in the story. The book, which won the National Book Critics Circle Award 1997, has been called Fitzgerald's masterpiece. In 1999 it was adapted and dramatised for BBC Radio by Peter Wolf.
A collection of Fitzgerald's short stories, The Means of Escape, and a volume of her essays, reviews and commentaries, A House of Air, were published posthumously.