Indeed, but that's only really because we've underfunded it. It wasn't so long ago (last labour government) that waiting times were reasonable, and it wouldn't take all that much money to fix.
Funding for the NHS has massively increased YoY. Ageing population is the issue and it's not as easily solved with money as you might suspect.
It still has one of the lowest per-capita budgets of healthcare systems in developed nations. If one wants to explain why wait times are high compared to other healthcare systems, that would seem a more obvious explanation than the single-payer funding model. I would agree that an ageing population is also a factor.