1881 Census
His daughter Hannah E (Eliza) is 18 [born 1861] Mary Jane is 17 [born 1864]
Fanny born 1867 has died 1873.
The witness at the marriage to Thomas Duck 11 March 1882 is Annie Eliza Brignall her sister Hannah Eliza who went by the name Annie.
So the parents marriage would be circa 1861 - William Agar to Jane Wood. _He was illegitimate
**William Brignall who died 28 June 1909 left a will, he was of 32 Tees Street, Loftus, Yorkshire. Executors are George Brignall, Mines Deputy and William George Duck, grocer's assistant.
Ref: Probate Index
Perhaps the will can provide further clues.
His wife Jane had died 1904.