Hi Simon,
Firstly just to let you know you'll find out more about common-law partner sponsorship over at
http://www.canadavisa.com/canada-immigration-discussion-board/family-class-sponsorship-b5.0/Secondly, I'm also English with a Canadian boyfriend and we've recently applied for common-law sponsorship after spending a year in New Zealand together on working holiday visas. We had lived together in Canada for 3 months before that - when I was on a WHV - but then spent 10 weeks apart while I went back to the UK so obviously we couldn't count that anymore! Anyway, you should be fine, but if you can find an employer while you're in Canada on a WHV who will sponsor you for a Temporary Work Visa then you can stay in Canada legitimately while you apply for PR (this is what I'm trying to do). Either way you will have a year living together so you should be okay. Just make sure that the moment you arrive in Canada you get a joint bank account, share bills (keep copies of everything) and keep ANYTHING and EVERYTHING related to your relationship - anything you buy together, receipts for trips you take together, take lots of pictures of you together - it'll make the application much easier when you come to do it.
As for how long, it's a bit of a piece of string job, but the London office isn't too bad apparently. It's much faster than applying as a skilled worker though. I'm anticipating around 6 months, but our case is fairly straightforward - yours should be too unless you've been in jail or bankrupt or something! We already have first stage approval after 2 months, which is that my partner has been approved as a sponsor, but now our paperwork is in London and my side of it is being processed.
I would recommend reading through all the forms and stuff now - print them off and start reading and absorbing them - I had them for a year before I sent the application and I can say that it was only towards the end - and after reading everything I could find related to it - that I began to understand it all!
Best of luck and see you over on the Family Class side soon!