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Born in Melbourne, Victoria, the son of Irish Catholic migrants; baker James Fingleton and his wife Mary, the Fingletons moved to Sydney in 1878 before the deaths of his parents left Fingleton orphaned at an early age.
After a limited education, Fingleton gained work with the New South Wales Railway and Tramway Department, initially as a tram conductor before his promotion to tram driver. Fingleton also joined the Australian Labor Party (ALP) and became active in the union movement, eventually becoming a union organiser.
He married Belinda May Webb in 1902 and together they had two daughters and four sons.
Fingleton was elected as the ALP member for the Electoral district of Waverley in the New South Wales Legislative Assembly in December 1913 and served until 1917 when, in the wake of the ALP split over conscription (which he opposed), Fingleton lost his seat in a landslide election loss to the conservative Nationalist Party of Australia.