Hi again Kate
Having found the above information and because we don't yet have the benefit of the 1911 census (until 1 January 2012) there is only one way of finding out for sure, who William's parents were - but that will cost you money I'm afraid - obtaining the birth certificiate! Unfortunately the records available via the Internet don't always cover some of the areas we need to enable us to pinpoint some of the finer details.
Of course, if we had for sure William's parents you will be able to push back further.
Sorry I can't seem to help more for you on this one at this stage. Do feel free to ask for more help though, if you do obtain a certificate.
Best wishes.
Kay
Manager