Well, at its heart, healthcare should be a basic human right, available to all persons on earth. From what I know there is no scientific or technological reason why that should not be the case already - it's merely a matter of logistics and political will.
WARNING UK SPECIFIC
I would reverse partial privatisation, agency staffing, consultants and managerial corporatisation (NHS Commissioning Board, Moniter etc.) that are essentially interesting (yet costly!) failed experiment at best. Create a well-funded non-profit pharma company under public (in a matter of speaking) hands, that will be (less) free of the shenanigans that go on under private care (obviously new public behemoths should be avoided, but ... ). That would free up funding for the many diseases that are chronically underinvested in, and allow private pharma companies to focus on the stuff they prefer to study for).
There is a lot of legislation you also need around the regulation of medical studies - existing regulation from journals and university boards are weak and fail all the time.) Oh yeah and replace drug patents with a reward system, taking a huge wedge out of the cost of drug procurement, a rare interesting idea proposed by Bernie Sanders.
Smaller healthcare providers (dentists, clinics etc.) should be given incentives to form cooperatives. All essential medicine should be free at point of use (dentristry, social care, optics, prescriptions and mental health included); I have largely soured on means-testing in any capacity in the health service. Phase out PFI; and any debts incurred from that should be audited and centralised under the Treasury. Reintroduce elected Community Health councils to replace the trusts. They should be half elected by people, half by NHS employees.
Great post. I basically agree with all of this.