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« on: Friday 07 June 13 23:01 BST (UK) »
I assume that you have the birth certificate for Thomas Hulme Baldwin, from which you have worked backwards, and that has led you to look for an Albert Baldwin born in Halifax about 1862? There is no birth record that corresponds to that. As a complete aside when searching I did see a Prince Albert Edward Baldwin registered in Bradford in 1863!
Widening the search to bring in births back to 1850, shows that there is only one Albert Baldwin registered in Halifax, and that was in 1855.
I assume that you have his father's name from the marriage record that you have and if you search the 1871 Census for an Albert Baldwin living in Halifax (no age specified) with a father called Fred or Frederick, then there is only one result and that is the one that you found.
I am inclined to support your view that he was indeed a bigamist. By the way in 1911 Walter Baldwin could be found in Armley Prison! His brother John was married and living in Halifax, and I cant find Susan either in the census or the death records.