Margolyes was born in Oxford, Oxfordshire. She was the daughter of Ruth (née Walters; 1905–1974), a property investor and developer, and Joseph Margolyes (1899–1996), a Scottish physician from Glasgow. She was grew up in a Jewish family and her ancestors are from Poland and Belarus. She is a lesbian and has been with her partner Heather for over forty years. She has also been an Australian citizen since 2013.