Its interesting that many people point to places like Sweden and Nordic countries as how the state system should work.
Whilst its only a small amount, if you visit a doctors, need an ambulance or require a stay in hospital in Sweden there is a small surcharge. To see a doctor costs between £8 and £30 but its capped in any 12 month period to around £90 in total. Hospital stays are around £10 per night. There is also a cost for an ambulance on top if one is needed but once again its capped.
There's are no cost if you're under 20 or over 85.
It does make you wonder if by doing something similar it would cut down on people making unnecessary calls. I know a few who work in A&E who have told me anecdotally of people going with a headache and being given a couple of paracetamols, plus those who decide to drink to excess or come unstuck doing "recreational" drugs who then require treatment would at least be paying something back.
Whilst its not the sole answer, the money might allow us to improve the healthcare system, however it would also need more taxation on top to achieve the same doctor & hospital bed ratios per person as Sweden, which is roughly twice as many as the UK.
Update... Just had a look and there are 1.38m doctors appointments per day in the UK, if only 500k were eligible to pay at a figure of £10 per appointment that would over a year (based on 260 working days) equate to £1.3Bn. I dont know the exact figure but lets say a doctor costs the NHS 200k per year, thats 6500 extra doctors you could have or probably three times that many nurses.