Does marriage cert give father's name? If so, I'd search for Charles H with that father's name on the 1901 census. All depends on whether you have a name for his father. If you don't try assuming he was named for him - or his middle name which might be Henry or Huw (given the fact that there are Morris in Wales)
As he married in 1915, if you don't already have them, his army records might be worth looking for in Kew.....Have you tried searching the National Archives website?
Just did a very quick search found 2 possible medal award cards:
Description
Medal card of Morris, Charles H
Corps Regiment No Rank
Royal Field Artillery TF 681656 Bombardier
Royal Field Artillery 293127 Bombardier
Date 1914-1920
Catalogue reference WO 372/14links to the Catalogue
and
Description
Medal card of Morris, Charles H
Corps Regiment No Rank
Royal Field Artillery 58570 Serjeant
Date 1914-1920
Catalogue reference WO 372/14links to the Catalogue
You can download pdf of each for a couple of pounds.
I searched here and put in name and regiment (RFA) under Corps:
http://www.nationalarchives.gov.uk/documentsonline/browse-refine.asp?CatID=10&searchType=browserefine&pagenumber=1&query=*&queryType=1
You have his service numbers - you should be able to find out more.
Good Luck