Oh. You are thinking of secondary effects of high-tax societies, such as flatter wage structures influencing (production) costs of healthcare. Yes - I absolutely agree that is a factor, and I genuinely believe that if the US wants to see the full economic benefits of single payer they must also make higher education cheaper, reform the malpractice legal frameworks, and so on. The fact that I tax-pay my doctors MD likely makes less of my tax money go to healthcare. Agree.
The UK does have a good single payer system and not (entirely) free higher education, so they naturally have more wage inequality (for other reasons as well including much weaker labor unions and labor laws) and should be a better comparison than e.g Scandinavian countries which has flat wages and tax-funded everything. Canada seems similar (tuition there seems to be around 50% subsidized?)
The UK does have a good single payer system and not (entirely) free higher education, so they naturally have more wage inequality (for other reasons as well including much weaker labor unions and labor laws) and should be a better comparison than e.g Scandinavian countries which has flat wages and tax-funded everything. Canada seems similar (tuition there seems to be around 50% subsidized?)