Hi,
I agree he appears to have a wife Hannah - per census information.
According to Civil Registration Births, there are two recorded in the Chesterfield Registration District, this
district includes births in Beighton & Eckington, which are possibly their children:-
March Quarter 1879 Chesterfield 7b 714 for a Henry Williams
March Quarter 1880 Chesterfield 7b 724 for a Joseph Williams
You would have to purchase one of these certificates to discover the maiden name of the Mother.
I cannot find a birth for a Frederick Williams, which suggest he was possibly born prior to the marriage,
if this is the case then he will be registered in the Mother's maiden name.
In what Registration District is the death for a John Williams aged 44 ?
Spendlove