Clive, where I wrote that William (& Frances) Moore called their only daughter Jane, this was wrong. I now have the 1861 census information which shows their first three children as Mary aged 4, Sarah aged 3, and William James Moor aged 11 months, all born in Cumberland. Only son William showed up on the next census.
I don't know whether the children's names in censuses help identify the correct father for William. As well as the above three, the other names were Benjamin aged 8, Isaac aged 3, and Joseph aged 1, in 1871, and John H. aged 8, Kendal aged 6, Francis R. aged 3, and Jane aged 8 months in 1881.
A grandparent's will quite often mentions the illegitimate child of a son, as does sometimes a father's one, if this was where you identified William Moore son of Robert M & Margaret CANNON as his father? I haven't researched any Moore families.
Sue