Travelling to another country for treatment sounds like the luxury to be honest. The unluxury would be no health care, or travelling 100 miles within the UK by train/bus.
I am contesting the "having" part of that sentence. The UK has problems, but it is not a country in dire straits.
To be clear: We are talking about GP right? To say get your blood pressure checked, or some mild antibiotics, or a rash cream, or referral to specialist? Not a specific treatment or surgery.
GPs gatekeep a most referrals, it's often virtually impossible to get any substantial treatment or surgery unless referred by a GP. Furthermore, for NHS treatments, it has to be a referral from an NHS GP, so you can't simply pay for a private GP to check something out.
Or, you can just wait for it to become bad enough that you go directly from A&E to inpatient care.
Having to wait 6 months is not as bad as having no other option. Although, I do empathize for your inability to go somewhere local and need of another option.