The soldier seems to be Harry Cox who was born in 1857, MMN Westall. This is the 1901 census entry and he is Harry on the marriage to Georgina in 1890:
https://www.ancestry.co.uk/imageview...ce&pId=9662373
Here are his army papers but the first page is very blurry (as are some of the later ones too):
https://www.ancestry.co.uk/imageview...rce&pId=764094
Age 18 in Feb 1874 whereas your Henry would have been 20. (Well, Harry would be under 18 but more likely to add years on than subtract them I should think.) Occupation before joining up - plater and plasterer.