The single key issue is the NHS being used as a political football. Constant reforms depending on who is in power, new Health Secretaries etc. These reforms waste money and destroy morale. The first step to creating an NHS to meet modern standards and expectations would be to create and independent advisory board, free of party affiliations. A mixture of medical, nursing, management, academic and ecomomic experts with the explicit purpose of maintaining an essentially free NHS.
That said, there does need to be consultation on how the NHS is used and what public expectations are. While modern medical advances are often artificially inflated in cost (and this should be addressed too) they are still high cost relative to when the NHS was created. I think the public need to see the difference between "lifestyle" issues which they should find privately and basic medical care which the NHS should provide. I work in mental health and it's incredible how many people think they should have therapy, like US style psycho-analysis, for emotional issues relating to their past..when really they are well, working etc...while this can be good for some people, it's just not something the NHS can or should provide. There are examples of this across all specialties.
Public dialogue needs to take place, again free from political persuasion, about what people are prepared to pay for. Most people could afford £5 to visit the GP, while most cannot afford £20,000 for some high tech cancer treatment that isn't approved by NICE. Perhaps the many paying a little, is better than the few struggling to pay a lot?
But ultimately, we need prioritised ring fenced funding for the NHS. Our current government seems to have the NHS low on its list of priorities. Anyone who can't see that the NHS is currently being allowed to fail, to benefit the few with an interest in privatisation is living in cloud cuckoo land.