I believe this is how the UK does it as well. You pay income tax, then you pay your NHS fee.
As I understand it, NHS comes from general taxation.
Obviously there is no actual "fee" to use the NHS at the point of use - it is all free apart from prescriptions which are the same price regardless of what you get (and you might get it for free anyway depending on your circumstances)
https://www.kingsfund.org.uk/projects/nhs-in-a-nutshell/how-...