Hi,
I am living locally to the Mow Cop area and Frances Brereton was my great great grandmother. Her b/cert shows her mother as Emma Brereton. Frances - dob 28th Feb 1868, place Mow Cop - was illegitimate - father unknown. Frances' mother, Emma Brereton, went on to marry Enoch Whitehurst and had 2 sons Enoch and Amos. They all appear in the 1881 census with Frances however, she is entered as Frances Whitehurst rather than Brereton - which is why you haven't been able trace her. Frances married James Beresford in 1888 after she also had an illegitimate child (my great grandfather Sydney Brereton in 1887). The father of Sydney is not known. Incidentally James Beresford had emigrated to Australia but returned to England after the loss of his wife and child. William Brereton dob 1806- Mow Cop - was the grandfather of Frances and he was married to Mary. In 1871 census Emma (daughter) and Frances (grandaughter) are shown in his household. I think the father of William Brereton is Abraham born 1786ish. Hope this helps.