The UK's problem is that it wants universal healthcare paid for by general taxation, and free at the point of use. However, the previous government wanted that whilst also reducing public expenditure. You can't have both.

It totally can be done, but it's expensive. I, personally, hope to see taxes rise to pay for this system to work as it should.

Private healthcare is already digging in its claws in the UK due to the fall in availability of state-provided care and (from my experience) it's not a good experience; and it's still expensive!

The UK's state provided system is pretty good, but it runs too much on good will right now.