Does your U.K. company have a Canadian branch that you'll be working from? IF so, problem solved. If not, then your U.K company needs to adhere to Canadian labor laws. You (and your U.K. company) will need to be concerned about potential tax laws. From a U.S. perspective, my understanding is that one cannot be a full-time W2 employee as a PR of Canada. I guess the equivalent for you is a U.K. P60 employee. You could deem yourself as a freelancer and invoice to your U.K. company, but then you should take measures so that Canada won't consider you a Personal Service Business (Google it). In summary, your options are...
1. Just let your current arrangement ride and cross your fingers that Canada won't take issue with this. Presumably, the U.K. will take tax withholdings and you'll hope that you can make use of the tax treaty and take a tax credit in Canada (where you'll report your worldwide income). In this scenario, the U.K. gets all or the bulk of your taxes. But someone on this board talked with a tax lawyer, and they were informed that they should make quarterly tax payments to CRA (i.e., for a period of time you'll be double taxed - paying withholdings to both the UK and Canada), and at the end of the year you'll try to claw back the taxes you paid to the UK through use of a tax treaty credit. So, in this scenario, Canada gets the bulk of the taxes.
2. Work with your U.K. company to make use of a Canadian cross-border Professional Employer Organization (PEO) - essentially, you'll work for the PEO who will lease you out to your U.K. company. Canadian labor and tax laws are satisfied. Of course, your U.K. company will need to be open to this and the associated cost.
3. Consider yourself a freelancer and invoice to your U.K. company for payment. This assumes that your UK employer considers you to be a freelancer and not a P60 employee. I don't think it matters if the funds land in a U.K. or Canadian bank, as either way you'll be reporting your world-wide income, and you should be making quarterly withholdings to CRA. Labor laws are a non-issue, as you'll be self-employed. For tax laws, you'll want to navigate the possibility that CRA will deem you a Personal Service Business, and this has potential negative tax consequences.
Finally, I'm not a professional accountant nor lawyer. My information is from my own personal research. I urge you to ultimately get professional advice.