Many thanks to willsy for good information which has helped to narrow down the search. It now seems to me that if it is correct that William and Sarah were indeed nephew and niece of Edward, then their father must have been his brother and it looks like there are only two candidates- John (aka John Isaiah with various spellings) and Thomas.
If it's John, then I've found him in 1891 and 1901 in Birmingham, and he died in 1922 in Aston (adjacent to Bham). I haven't found him in 1911 or 1921 so I suppose he might have been gone to America and then returned?
If it's Thomas then I can't find any certain record of him beyond his baptism on 1.1.63, and the most likely record might be the death of a Thomas Bennett aged 5 in 1868. However, that's just a death index record so no indication of parents.
It would help if the 1871 and/or 1881 census records could be found for John and Elizabeth, together with their sons John I and maybe Thomas. Their eldest son Edward was living with George and Mira Bates at this time. John senior had died by 1891 as Elizabeth is shown as a widow.
