Dalton has one son, Alexander (born 7 August 1997), by Russian musician Oksana Grigorieva. He was in a relationship with English actress Vanessa Redgrave (with whom he appeared in the 1971 film "Mary, Queen of Scots") between 1971 and 1986. Dalton is a Manchester City F.C. supporter. He is often seen at the City of Manchester Stadium to watch his team play. Dalton remains unmarried.