Which Christmas, this one or the next? There's no way you'll be a PR in Canada this Christmas. Even if you applied today, the first part of the process (sponsorship approval in Mississauga) takes about a month. London has been processing application in 2-8 months (see processing times here:
http://www.cic.gc.ca/english/information/times/international/05-fc-spouses.asp), so it would take a minimum of 2 months and that's assuming your application is complete, there's no questions needed to be asked, no documents missing and the background check is simple (the more countries you've lived in, the longer the background check takes).
You have good odds for next Christmas though

You can apply as a spouse at any time (you'd have to get married first of course

. To apply as a common-law partner, you'll have to wait until July when you will have the 12 month cohabitation needed to qualify as a common-law partner. Assuming everything goes ok with the app and you pay all the fees upfront, I don't see why you couldn't be in Canada by next Christmas. Keep in mind that processing times do change, but they won't suddenly jump up to a year minimum.
As for the white... eh, depends on where in Canada you are. I'm in the Vancouver area and I hear I might be missing out on the white this year

Oh, also... you know, just because the application is being processed in the UK it doesn't mean that you have to be in the UK. You are allowed to stay in Canada as a visitor. Well, in your case you might have to leave and come back as a visitor, but that's another matter. You wouldn't be able to work in Canada or get health insurance, but you could stay with your partner.