Born in Plymouth, Randall was educated locally and worked as a fitter in the city's dockyards. He gained a BSc degree in Electrical Engineering from University College, Cardiff and worked in the electronics industry for twenty years. He joined the Labour Party in 1966 and contested South Worcestershire at the October 1974 election and Midlands West at the 1979 European election before entering Parliament. He served as parliamentary private secretary to Deputy Leader of the Labour Party Roy Hattersley and as opposition spokesman on Agriculture and Fisheries and Home Affairs.