I'm all for a bit of charging in appropriate places, but the £8 per day in hospital idea seems a bit silly. It's an insignificant amount, firstly. Secondly, it's just an additional funding mechanism, which creates extra admin. It would be simpler and more sensible to just raise tax.
To illustrate what I mean by appropriate places, I'd see nothing wrong with GP services being paid for directly by consumers. GP's could charge patients the full cost, with government maybe paying 80%/90%/100% of the charge for anyone on Universal Credit.
The purpose of insurance (including social insurance) is to cover things people can't afford out of normal income, or even short-term savings, and for the vast majority of people, GP visits are are cheap enough to count as non-insurable expenses.
The reason it would be appropriate to charge for GP services is that then supply and demand would match, it would (eventually) completely eliminate the shortage of GP appointments.
The difference between charging for GP services and services your are referred to such as hospitals and specialists is that the consumer decides GP services and GPs are gatekeepers of other services. So there is control over appropriate use of other services, but no control over consumption of GP services. So charging for GP visits would serve a useful purpose, regardless of the impact on government/NHS finances.
The same arguments as apply to GP services could apply to ambulance services. (Although I suppose it depends on whether you think operators can triage calls to see if an ambulance is really necessary, if they mostly can then I guess that counts as a referred service that you don't need to control access to.)