Born on 24 December 1885 in Leeds, England, Heaps emigrated to Canada in 1911 and worked in Winnipeg as an upholsterer.

He ran for the House of Commons of Canada as a Labour candidate in 1923 in the riding of Winnipeg North but was defeated.

Heaps and Woodsworth agreed to support the Liberals in exchange for the government creating Canada's first old age pension.

One of the few Jews in Parliament, Heaps pushed the government to allow Jewish refugees from the Nazis into Canada, but with little success.

Heaps died in Bournemouth, England, on 4 April 1954 while visiting family and was buried in his birthplace of Leeds.