I'm not sure I understand your situation, you're moving but you haven't got visas yet? From the
UK the High Commission takes 15 months at least to process applications for skilled workers before you get the visa, from the date you submit all the paperwork to them.
Getting work permits is pretty straightforward, but yeah, major complaint immigrants have is that employers can't be bothered with anyone who doesn't have citizenship or permanent resident status, which is why there are so many immigrants with PhDs driving taxis. It's not even legal, but I've seen lots of jobs advertised with "citizens only" in them.
Human Resources Canada is trying to crack down on it. They have a website you can use with job postings on it, bit like the Job Centre in the UK.
If you've already applied for permanent residency I'm not sure how you're going to do this, because the High Commission assumes you live in the UK still, so if you apply for a work permit and enter Canada, that's going to make things complicated.
What they recommend at the moment is for people to come in on work permits and apply for permanent residency from inside Canada as work permits are faster to process, so it avoids the wait.
One piece of advice I can give you is that if you work in construction and civil engineering, Alberta is the place to move to, not BC. Unless you want to help build the tunnel near Golden, which is a major project.
The housing market in the US going down the tubes I reckon (and so does everyone else) is going to cause problems for the BC economy because of the lumber market. With oil at $130 a barrel, I don't see that happening in Alberta.
Also easier to get a work permit, plenty of employers around Calgary and elsewhere in the Province will hire anyone with a heartbeat, there's a massive labour shortage. I've met several Americans working here on work permits who work in construction.
Steve.