I have misunderstood your post. The sentence "however, it is socialized medicine, not all treatments are available" does rather imply an assumption of homogeneity.

Any legitimate medical (as opposed to purely cosmetic or entirely non-essential)treatment available privately in Britain is also available on the NHS. As in the US, you may have to travel to a specialised centre to get it. The surgeon operating today on the Arabian prince is likely to be performing the same surgery tomorrow on the poor Bangladeshi waiter from the back streets of the East End - often in the same hospital, using the same equipment and assisted by the same team.

If you pay for private medicine, what you mainly buy is more luxurious surroundings, not superior care.