Can you take a rental car from the US into Canada if you are a UK citizen?

It would depend on the policies of the company you rent the car from. As long as your driver license is valid, getting the car shouldn't be a problem. Whether you can drive it out of the US and into Canada is something you need to specifically ask the rental agency.

There may be a mileage limit on your rental (which you can pay to extend). There may also be rules about crossing state and/or country borders. Again, ask the agency.