Hello Jarlath
Thanks for going to all that trouble - I really am very grateful and now at least realise why I have been stuck at William in the family tree for so long.
Both of your possible explanations are likely to be correct. However, there is a third - Nancy was known to the later Teals only as "Miss Teal", so it is also possible that she was a relative (Aunt?) who took William in when James and Elizabeth stopped looking after him. Of course, it's also conceivable that she actually was his mother and he was born out of wedlock and lived with James and Elizabeth in his early years for some reason.
Anyway, I'll try and get my hands on copies of the censuses as you suggest and start delving again.
Thanks once more for all your help.
Regards,
Andy Teal
ps I have some info. on Isaac Bancroft if it would be of any use to you or anyone visiting your Web Site.