The public attitude to the NHS in Britain has tended to place it in a quite separate category from other sectors formerly in public or government ownership. The theoretical and practical advantages of privatisation have been accepted far more widely in those other sectors than they have been for the NHS. That’s why Margaret Thatcher famously (or notoriously, depending on your point of view) once said ‘the NHS is safe with us’. To have said anything else would have been political suicide, for she knew any hint of privatisation would have alienated her own core Conservative vote.
Why is this so? I think that emotionally, at least, we have tended to see the NHS as belonging in the same category as the armed forces: as part of that irreducible core of state provision which is a legitimate justification for taxation. Both have been seen as necessary to defend the people from its enemies - in the one case military, in the other biological. You would no more expect a private service to protect the nation’s health than you would a a private army to defend the its borders. Though the reasoning may not have been articulated in that way it was, I think, the assumption underlying the public attitude; and that which made it acceptable for voters who believed themselves to be consistently conservative.
Only “political suicide” due to the number of liberal Tories that wanted to keep the NHS around. Just as bad as, if not worse than, the GOP establishment.
BTW, the same liberal Tories stabbed Thatcher in the back when it came to surrendering more sovereignty to the European Union.