Born in Bradford, Mitchell was educated at Woodbottom Council School, Bingley Grammar School, the University of Manchester and Nuffield College, Oxford. From 1959–63 he lectured in history at the University of Otago in Dunedin, New Zealand. He was a journalist at ITV company Yorkshire Television from 1969 to 1977, presenting their regional news programme Calendar, although he spent a short period at the BBC in 1972. During his period at Yorkshire, he chaired a live studio discussion featuring a debate between Brian Clough and Don Revie on the day in 1974 in which Clough had been sacked by Leeds United. He was elected to Parliament as MP for Great Grimsby at a by-election in 1977, following the death of the previous MP, the Foreign Secretary Tony Crosland.