Often illegitimate children 'invented' a father at time of marriage. It's a bit embarassing when the vicar asks "Father's name?" when the new wife's relatives are all in attendance!
I have now found burials for the WATERFIELDS:
William WATERFIELD Ford Park Cemetery Burials, Section E, Row 5 Loc 6 A/C 1015/2, 4 Jan 1863. Of Lower Batter Street, aged 83.
Elizabeth (Mother) WATERFIELD Ford Park Cemetery Burials, Section E, Row 5 Loc 6 A/C 1015/2, 7 May 1865. Of Lower Batter Street, aged 80.
Mary WATERFIELD (sister of Elizabeth Martin) Ford Park Cemetery Burials, Section E, Row 5 Loc 6 A/C 1015/1, 29 Jun 1856. Of Lower Batter Street aged 39.
Elizabeth WATERFIELD Ford Park Cemetery Burials, Section E, Row 5 Loc 6 A/C 1015/2, 11 Sep 1864. Of Lower Batter Street, aged 45.
I am awaiting a copy of the marriage certificate between Thomas SQUANCE & Elizabeth M. WATERFIELD (1834).