Hi songbird82,
I started responding to the PM you sent me, which was pretty much verbatim of your post, then realised you'd also posted here, so I'll just respond here. (FYI, better to keep questions public - one, others can benefit from the answers, and two, my answers can be vetted by others - we don't get it right every time!)
Basically, Andrew's answer completely mirrors what I was going to say. The answer to the Mississauga/London thing is in the FAQ which Andrew has linked you to, so have a read of that and it should answer your question. In addition, the cover page on the spreadsheet has a big red box that also answers this question. (I'm running out of ways to make that box more obvious!)
I am also curious as to why you bothered to get your MP involved - I wouldn't get your MP to do anything else for you until you're at least one year into the process, there's no point otherwise.
And Andrew is correct, sometimes applications change visa offices. We don't know the reasons - none of us works for CIC! - but a few people have had their office change. My guess (and it's only my guess!) is that it has something to do with background checks that can't be done from outside of the UK. I know in Canada a handful of people get requests to have RCMP checks done while the vast majority do not, and this usually results in "ZOMG I AM FREAKING OUT WHY DO I NEED TO DO THIS I AM NOT A CRIMINAL IS CANADA GOING TO ARREST ME OMGOMGOMGOMGOMG *FLAIL*".... and it's usually because the standard background check came up as inconclusive, usually because of something simple like the applicant happens to share a name and birthday with someone who DOES have a criminal record in Canada, so they ask you to do an RCMP check which includes a fingerprint, then they can be sure you are who you say you are. It's not a big deal, it's just an extra wrinkle that takes an extra few weeks to iron out. I suspect - again, only my guess - that applications that start in Mississauga but get transferred to the UK after have something similar happen.
Finally, if you look at the spreadsheet, you can see that tons of people are processed in London from the get-go and not transferred... not everyone's applications stay in Canada. So just calm yourself and sit back and wait it out. Average for London for British applicants hasn't changed in the past 1.5ish years, it's been holding pretty steady at 8 months. The advertised 29 months is because of the applications from Islamabad. (This is also explained in detail on both the cover page of the spreadsheet and on the FAQ.)
Hope that helps.