Not sorry I asked, though I'm not sure I offered - I expected it was something I probably couldn't help with, but thought someone else might be able to (LC members being generally knowledgeable, and usually helpful if they can)! But let's have a look. (By the way, I have Savages in my data: James of minimal data, Edward born 1631, his daughter Maria baptised 1675 Staffordshire, and another Maria daughter of the above James, she born 1854 Norfolk died 1929 Australia. I'm particularly fond of her marriage, as it's between Savage and Slaughter! Happy to share details of any of them.) Yes, your suggestion of "the opportunity" seems possible - she'd have been about 23 and he about 43 in 1911, but of course we don't know how long she'd been a servant by then - might have been earlier when she was younger. Or later; if the daughter was 4 in 1921 that gives us 1917 or '16. Hmm, during WWI. What sort of address was where she was a servant in 1911 - just a private house, or some sort of stately home/mansion/whatever? (Or something like a hospital, or other place of large employment?) If by any chance any of the latter, might be a source of records to search (employment records etc.; maybe also wartime records of all sorts - including newspapers). The age difference also supports your suggestion that it might be the son. (Though whichever, the family line would be similar, the only question being whether the son's mother is an ancestor.) You say you don't know where she was born: I take it you don't believe the place shown in the 1921 census. Do you know the date of her birth (her birthday for the date [possibly from the 1939 register - check there anyway], and did she know how old she was to clarify whether the year was 1917 or 1916)? I don't know if it's possible to find all the people born on a given day.
Frustrating that the Canadians aren't interested; best hope is maybe that other relatives do a test. I presume you've checked e. g. familysearch to see if the Savage or Moxom families have any other relations (or even if the clandestine relationship can be confirmed [or at least corroborated]).
So - hope I've maybe given you some thoughts of places to look - though I suspect you've already thought of them. But maybe also someone else here can help. You may also like to try other parts of these forums: I don't really know my way round them. I'd also definitely try the newsgroup soc.genealogy.britain, but I know most people these days don't use (or even know about) newsgroups.
Good luck!