The seat had become vacant when the constituency's Labour Member of Parliament (MP), John "Jack" McCann (4 December 1910 – 16 July 1972), died.

He was first elected in a 1958 by-election following the death of the sitting Conservative MP Wentworth Schofield.

The list below is set out in descending order of the number of votes received at the by-election.

Smith won the by-election and retained the constituency until he retired from Parliament in 1992.

Jim Merrick, the chairman of the British Campaign to Stop Immigration, was from Bradford and issued leaflets headed "Enoch is right".