My gg-grandmother was Mary Farlow, daughter of James and Catherine.
I believe Mary was first married to a man called Bruce, Henry and Vincent were not illegitimate as far as I am aware. She was widowed when she married Thomas Hancock, as my g-grandfather Samuel Godwin Hancock's birth certificate refers to her as 'Mary Farlow, late Bruce'. I understood this to indicate a widow, though I have never bothered to look for her first marriage.
Vincent and Henry were baptised at Stone in Staffs. They seem to have taken the name Hancock on the 1881 census. My granny (who died earlier this year) told me they had both emigrated to Australia.