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A Glasgow Hillhead by-election was held on 25 March 1982. The by-election was caused by the death of the Conservative Party Member of Parliament for Glasgow Hillhead Tam Galbraith on 2 January 1982.
Hillhead had been held by the Conservatives at every election since its creation in 1918. Galbraith himself had held the seat since the Glasgow Hillhead by-election, 1948. However, his majority had been gradually reduced, and even in the 1979 election which the Conservatives won, the Labour Party had continued to gain ground.
The Labour Party had suffered a split in 1981, with the Social Democratic Party (SDP) formed by the "Gang of Four" prominent figures: David Owen, Bill Rodgers, Shirley Williams and Roy Jenkins. The SDP had several Parliamentary seats held by defectors from Labour, and one by a defector from the Conservatives, while Williams had won the Crosby by-election, 1981 for the party, leaving Jenkins as the final "Gang of Four" member without a seat in the House of Commons. He contested the Warrington by-election, 1981, coming a close second, and remained keen to fight a winnable seat.