Hello, Andrea. I saw that you have no replies.
To recap. George Bambury/Banbury was born c.1850/1 in Ireland. Father was George, mother Ellen. Ellen was born c.1833 Ireland. George senior was a soldier. You don't know religious denomination of the family but you are inclined to think they were Protestant. George junior and mother, Ellen were in England in 1861 and George junior was still in England in 1881. George junior's birthplace was down as Castlebay barracks on 1881 census.
Have you found George junior or either parent on any other census?
Do you have his father, George on a census? If he was in barracks his full name may not have been recorded. Was George senior born in Ireland? You know he was at Stafford at the time of his wife's death. Do you know his regiment? Did he re-marry after Ellen's death? When & where did George senior die?
Did George junior have siblings? What information do you have about his marriage?
Do you have evidence to suggest the family may have been Protestant?
Baptism register 1838-1855 for Castlebar, Aglish and Ballyhean Catholic parish is on National Libraries of Ireland website.
Civil marriage registration for non-Catholic marriages began in Ireland 1845. I don't see a marriage for George Banbury in Ireland 1845-1855 on Irish Genealogy website.
These are 2 websites about army establishments in Ireland.
Army Barracks of 18th century Ireland https://barracks.18c.ucd.ie
You'll see from the accompanying map that there were a lot. Many would still have been in use in 19th century.
Another website is Irish Garrison Towns irishgarrisontowns.com This has frequent updates.
Did none of the family include county on any census? A head of household was responsible for filling in the schedule. Information from completed schedules was copied into census enumerator's books. Errors could have happened at any stage. There is Castle Bay, near Rosscarbery in County Cork, and Castlereagh. S Wilson's website has a placename search facility. If George junior left Ireland around age 10 and didn't live there again, he may not have had an Irish accent by the time he was 30, unless he lived or worked among Irish people.