Luckily, you can safely ignore those views; they are both economically and politically illiterate.
There is an assumption abroad that things like public health services are inefficient and so we only fund them out of decency. This is widely assumed by lefties who wish to assume that righties want to abolish the the whole concept out of indecency.
But any righty with a basic understanding of economics 101 knows that insurance works better if everybody buys it (due to a concept called
Adverse Selection), and thus switching away from single payer insurance wouldn't lower costs, it would raise them. Adverse selection is one of the great inefficiencies of the American health care system that even the most rabid Tory would not wish to recreate.
So you see, while it makes sense for both right and left to wish to change how the NHS delivers the actual services such as hospitals and clinics and drugs and what have you. Neither side has any motive to change how it is funded in any significant way.
Politically, if the Tories were to privatise health insurance, that would be their last act. The party would immediately dissolve because the elderly people who have voted for them would be the ones whose insurance premiums would be highest for obvious reasons. So as a policy, it only makes any form of sense if that policy is the entire purpose of the party. It would make sense for UKIP to destroy itself through victory over Europe, but not for the Tories to dismantle themselves through a suicidally stupid health policy that their successors would immediately reverse anyway.
In short. The Tories dismantling the NHS isn't a Tory wet dream, it is a Labour fantasy.