His son Brian is a successful businessman and a former director of Celtic F.C.. His brother John Dempsey (Bellshill) was a footballer for Ipswich town (England), Hamilton, Queen of the South, Newry Town (Ireland) and Cowdenbeath. John was also a football scout after his playing career, with Hamilton Academical, and more famously Glasgow Celtic for 11 years; from 1965 to 1976 he served under the late Jock Stein during the club's win in the 1967 European Cup Final.