I would perhaps be suspicious that James Jordan doesn't really exist as George's father.
On the 1881 census, I think I have found George in the household of his older brother William. His mother (Eliza C Jordan) is also there RG11; Piece: 2999; Folio: 6; Page: 5
We can trace Eliza, William and George back to the 1871 census RG10; Piece: 3122; Folio: 80; Page: 24
That is obviously the earliest census with George on, but we can look at Eliza and William in 1861 RG 9; Piece: 2160; Folio: 26; Page: 4 and see that they are with Eliza's parents - father's name is James, and he is a tailor. It might well be that Eliza got pregnant outside of wedlock, and that when George came to get married himself, he gave his grandfather's name to give him an air of respectability.