Me again, and am confusing myself going round in circles. If it is any help at all, your James Bradford is on the 1861 census in Bermondsey (where his daughter Emily was born) living with his wife Anna.
Full details:
Little George St, Bermondsey
James Bradford 25 M Leather dresser bn Devon Exeter
Anna Bradford 21 M Straw hat maker bn Bucks Aylsbury
Class: RG9; Piece: 322; Folio: 172; Page: 39;