- She was awarded the 1981 London Evening Standard Theatre Award for Most Promising Playwright for "Steaming".
- Daughter of Sir Philip Gordon Dunn (d. 1976), second baronet.
- Cousin of Danny Moynihan.
- Was elected a Fellow of the Royal Society of Literature in 2004.
- Dunn was educated at a convent up to the age of 14. She and her older sister Serena were evacuated to America during the Second World War.
- Studied at the Courtauld Institute of Art.
- Worked for a time in a confectionery factory in Battersea.
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