In Canada you have basic health care coverage but it covers all aspects and procedures including “serious procedures” just maybe not in a fashion that is expedited. The more serious the issue the quicker it is taken care of - the same as in UK. If you purchase a supplemental HC coverage, you’re moved to the front of the queue, more or less.
I’ve never heard in either country some being denied service because they only have basic coverage under Single Payer forcing a patient to travel to another country for a procedure.
Elective surgery is not the same as basic coverage.