Quigly was subsequently educated at Godolphin School, Salisbury and, having "won scholarships from five different bodies", went up to Newnham College, Cambridge.
Her most notable translations are Silvano Ceccherini's The Transfer, for which, in 1967, she won the John Florio Prize, and Giorgio Bassani's The Garden of the Finzi-Continis.
According to Robin Healey's Twentieth-Century Italian Literature in English Translation, Quigly was one of the top 10 translators of Italian literature of the last 70 years, alongside Archibald Colquhoun, Patrick Creagh, Angus Davidson, Frances Frenaye, Stuart Hood, Eric Mosbacher, Raymond Rosenthal, Bernard Wall and William Weaver.
[4] The Eye of Heaven was autobiographical, based on Quigly's "impulsive and ultimately ill-fated marriage" to "impoverished but aristocratic sculptor" Raffaello Salimbeni, of Sienese origin and ten years her senior, whom she had met and fallen in love with when in Florence.
Quigly and her son, Crispin, shared a close bond, working together on property renovations in Cambridge during his time as an undergraduate there, and later in south-west London.