Dempsey was educated at Holy Family School, Mossend, the Co-operative College in Loughborough, and at the National Council of Labour Colleges. He was a clerk with a haulage firm and a councillor on Lanarkshire County Council from 1945. He later worked as a lecturer on political economy and a writer on local government.
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), Cowdenbeath. John was also a football scout after his playing career with Hamilton Academical and more famously Glasgow Celtic for 11 years; 1965-76 serving under the late Jock Stein during the club's win in the 1967 European Cup Final.
- Leigh Rayment's Historical List of MPs – Constituencies beginning with "C" (part 5)
- Times Guide to the House of Commons, 1966 & 1979
- Hansard 1803–2005: contributions in Parliament by James Dempsey
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