Swinton was born in London. Her mother, Judith Balfour (née Killen), was Australian, and her father, Major-General Sir John Swinton of Kimmerghame, Berwickshire, KCVO, is Scottish. The Swinton family is an ancient Anglo-Scots family that can trace its lineage to the ninth century. Swinton attended West Heath Girls' School (the same class as Diana, Princess of Wales), and also Fettes College for a brief period. In 1983, she graduated from Murray Edwards College (known previously as New Hall) at Cambridge University with a degree in Social and Political Sciences. She has two Honorary Doctorates: one from Napier University in Edinburgh, received in August 2006 and one from the Royal Scottish Academy of Music and Drama (RSAMD) in Glasgow, received July 2006. She was a contributing editor to the literary magazine Zembla.