Initially a member of the Independent Labour Party, Gilzean joined the Scottish Socialist Party split in 1932, and was elected as its vice-chair. This organisation affiliated to the Labour Party, for which he unsuccessfully contested Edinburgh Central at the 1935 general election, winning 41% of the votes. He won the seat in the Labour landslide at the 1945 general election with majority of 4,220 votes, becoming an MP for first time at the age of 67.
Andrew was married to Annie Thomson (1877-1965). Both were cremated at Warriston Crematorium and a plaque to their memory exists in the southern arcade.
- The National Union of Conservative and Unionist Associations, Gleanings and Memoranda (1932), p.500
- Craig, F. W. S. (1983) . British parliamentary election results 1918-1949 (3rd ed.). Chichester: Parliamentary Research Services. ISBN 0-900178-06-X.
- "UK General Election results February 1950". Richard Kimber's political science resources. Retrieved 28 March 2009.
- "UK General Election results October 1950". Richard Kimber's political science resources. Retrieved 28 March 2009.
- Hansard 1803–2005: contributions in Parliament by Andrew Gilzean
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