They spend a great deal of money on the system.
Indeed, not only UK but many other EU countries have nationalized healthcare and spend a lot of tax money on it. However, you should well understand that spending money on something does not mean that you'll get that money's worth of service.
Which is, sadly, the case with most nationalized healthcare systems.
That money just kinda evaporate on the way from the treasury to the patient. Months of waiting time for not-so-big procedures, medicines denied because some jobsworth in the ministry decided people having some disease are too costly to save (or because manufacturer did not bribe correct people)... It's slightly better than not having any health coverage at all, but far far far from being good. Hell, for the same amount that I pay in health tax I can get private coverage, where not only specialist diagnosis is next day, but also I'm treated as a valued customer instead of being considered some loser who bothers the staff.
(OK, not all this happens specifically in the UK, but I have no reason to believe it's that much different from my country - UK's healthcare is probably better as it is richer country, but still...)
No system is perfect, I hear many Americans wanting nationalized care and not a small number of EU people hating it. If you ever invent a system where everyone will be happy, you'll have a monument in every city ;-)
