Probably your best avenue is to trace his marriage to Elizabeth and purchase a copy of the certificate which will give you his father's name and occupation. You then may be able to trace him with his parents in 1841 or 1851. A possible marriage is with Elizabeth Hardy in Chelsea Dec.1859, 1a, 309.
Looking for the birth of his son John, however, the most likely is in Chelsea, Sep.1859, 1a, 164. This is before the marriage to Elizabeth Hardy and therefore should have been registered in the mother's name, therefore the marriage may have been earlier. It may be necessary to purchase John jnr. birth certificate in order to obtain Elizabeth's maiden name and then trace the marriage.