This may not take you any further forward but I found your William Anthony in the 1871 census of Codnor Loscoe at RG10, Piece 3476, Folio 51, Page 45. I have the image (pdf 440Kb) if you are interested.
I am looking for William Anthony a boatman married to
Hannah (prob nee
Caladine) with children William born
Armitage Staffs c 1815, Thomas born
Armitage Staffs c 1818, Samuel born Ironville Derbys c 1824, Thomas born Ironville Derbys c 1827 and Henry born c 1829 Ironville Derbys. Have you come across him in your research?