Born in Doncaster, West Riding of Yorkshire, Concannon was educated at Rossington Secondary School and through the Extra-Mural Department of the University of Nottingham.
He worked as a miner and as a National Union of Mineworkers (NUM) official.
Under Harold Wilson and James Callaghan (Prime Minister from 1976 to 1979), he served as a government whip and as Northern Ireland minister, and was appointed a member of the Privy Council in 1978.
A serious car accident led to his retirement as MP for Mansfield at the 1987 election; Alan Meale succeeded him in the seat.
Concannon died in Mansfield on 14 December 2003, aged 73.