I have a theory BUT would need marriage details to confirm her fathers name.
In Higham Ferrers in 1841 are a William Coles, blacksmith, Sarah Coles, Mary Jane 2 and a Martin Coles (presumably father of William). GRO index shows birth of Mary Jane in Dec.qtr.1838 Wellingborough with mmn of Spong.
William Coles married Sarah Spong 11/11/1832 Higham Ferrers.
There is no baptism for daughter Mary Jane - however, there is a baptism for a Sarah Jane 26/4/1846, dau. of William, blacksmith and Sarah but no corresponding birth entry for around 1846.
I then discovered that William was buried 14/9/1847 HF, wife Sarah 30/5/1844 HF and Martin Coles also buried in 1844. So, was Sarah Jane bp'd 1846 (for whom their is no birth entry) actually the Mary Jane born in 1838 who's name got changed along the way, and after death of his wife William decided to have the daughter baptised. Have looked at original parish records for HF and none of the entries give an indication of how old a child was at baptism (which they often do).
I feel sure that Sarah Jane is connected to this family and that she is in fact the child registered as Mary Jane in 1838, baptised in 1846 as Sarah Jane when 8 years old after the death of her mother. An orphan by 1851 who seems to have been the only child.
Everything hinges on details on marriage for Sarah Jane's father - if William, blacksmith, deceased then I feel the above scenario is correct.
Annette