If you have a UK passport, you should be allowed to visit Canada without a visa anyway, and once you're here, CBSA can see in their system that you are a PR. (Bring your COPR too just in case.)
Some airlines want to check that you are allowed to enter Canada (I believe the onus is on them to check before letting a passenger fly and if the passenger is refused at the other end the airline has to fly them back.) and I don't know, if you tell them you are a PR, they Might demand to see your PR card. I'm not sure it will be an issue with your airline or not. (I'm also visa exempt (Japanese) and Air Canada has never asked me about my visa when I boarded a flight to Canada from Japan. They probably assumed I was ok.) So I think it will be ok. Or should be ok - you should be able to argue your way through, because CBSA will know that you are a PR, even without your PR card.