Margaret Natalie Smith was born in Ilford, Essex, on 28 December 1934. Her father, Nathaniel Smith (1902–1991), was a public health pathologist from Newcastle upon Tyne who worked at Oxford University; her mother, Margaret Hutton (née Little; 1896–1977), was a Scottish secretary from Glasgow.
During her childhood, Smith's parents told her the romantic story of how they had met on the train from Glasgow to London via Newcastle. She moved with her family to Oxford when she was four years old. She had older twin brothers, Alistair (died 1981) and Ian. The latter went to architecture school.