Hello, Angie
Is this your Edwin Rodds in the 1881 census as his place of birth is shown as Islington not Birmingham, & was living in Kettering, Northamptonshire.
Rg11/1575  folio 45  page 37
54 Alexander St, Kettering, Northamptonshire
Edwin Rodds,  age 22   Baker   b  Islington
Lucy Hardman Rodds  wife  age 21  b  Mosely, Birmingham
Frederick  son  age 3 mths   b  Leicester
Birth
Edwin  Rodds
Sept.  ¼  1858  Islington  1b  215
Marriage
Edwin Rodds =  Lucy Hardman
Dec ¼  1880   Birmingham  6d  87
Nothing could be found for Edwin, Lucy & Frederick in the 1891 census not for Edwin & Frederick in the 1901.
Meliora