Here's the 1911 Census record:
http://issuu.com/garagecollective/docs/davidson_1911It's the only one I've got in full. The rest were free index searches on familysearch.org, concentrating on the John Thomas' I could find. But where I must have gone wrong was not noticing that he was born in London, not Manchester like the rest of the family.
The Thomas Davidson listed in the 1911 Census came to NZ in 1920 with the Bateman's. This seems to match up to what we know of Thomas, my g,grandad, but he never said why he came to NZ or ever talked about his parents.
FreeBMD & Lanc BMD records a John Thomas DAVIDSON & Annie LISTER as marrying in 1905, Chorlton at the Registrars Office. There is a Thomas DAVIDSON birth registered in Chorlton in Jun Qtr 1907, which appears to match up.
However I should note that I haven't got a birth or death certificate yet for Thomas, which I'm in the process of doing. So its not proven that the Thomas on the 1911 Census is definitely my g.grandad...