Hello Rosie,
No, I'm certainly not giving up, hence my comment I'll just have to carry on looking and hoping.
Since making my original post I have noticed the Rootschat policy regarding the 1911 Census:
RootsChat's position - under guidance from the management - is that we cannot allow look-ups for the 1911 census either to be requested or offered.
This census is exclusively available online and anyone responding to a request or offering a look-up is technically breaking the terms and conditions of their subscription with whichever provider.
and I have no wish to encourage anyone to go against the policy.
But back to what can be discussed. The details that you show for 1901 are for the family that interest me but those from Familysearch must, I think, refer to a different family as William Snr would be 32 in 1911, was not a widower, and, as far as I've been able to trace, did not have a daughter named Alice, although it's interesting that his occupation is cited as cycle polisher (see below).
Your suggestion has opened up a line of investigation that I had not considered, that of a truncated surname, although I have looked at alternate spellings, and I thank you for that.
William's 1920 death certificate gives the following information:
Age 42 of 7 House, 2 Court, Stafford Street, Wolverhampton. Ex Private South Staffordshire Regt - 241258 formerly a cycle fiter[sic]. Died of (1) Shrapnel wound shoulder left Bronchiatosis (2) Cardiac Failure. No P.M. Informant was Mary Ann Brittain, widow of deceased in attendance, same address.
I am still keen to receive any suggestions/help that may be offered and did not intend to close my query.