Thank you all, esp. for the internet resources, yet to check them out.
Yes, I have looked at family trees on Ancestry, seemed like a good resource. Yes, Neale1961, now I am not sure if the William I have been tracing is actually the one who wss my gg. grandfather. If it turns out that way, I am sorry you have all been to so much trouble over it.
I have spent a lot of time looking for William and his daughter Lily. with nothing definite forthcoming, it seemed that if either of them could not be found, then maybe they had moved out of UK. Then it made sense that either they arranged an expensive and disruptive voyage themselves, or that they may have been transported here (to Aus).
Will follow up all your idess, thanks, lasswade.