A by-election was held for the United Kingdom Parliament seat of Birmingham Hodge Hill, on 15 July 2004. The by-election was called following the resignation of Labour Party Member of Parliament (MP), Terry Davis, on 22 June 2004. Davis had been appointed as Secretary General of the Council of Europe. The by-election was held on the same day as the Leicester South by-election, which saw Labour lose the seat to the Liberal Democrats on a 21% swing.

Terence Anthony Gordon Davis is a British Labour Party politician and businessman. He was the Member of Parliament (MP) for Bromsgrove from 1971 to 1974, and for Birmingham Stechford and its successor seat, Birmingham Hodge Hill, from 1979 to 2004. He was then Secretary General of the Council of Europe from 2004 to 2009.