the NHS in the area in which I've been living for nearly a year now (and my father for three, he moved out earlier than the rest of us from Greece) has been pretty decent - no waiting lists and some very nice and friendly doctors. Perhaps its my relative bias comparing everything to the shithole Greek healthcare was turned into after austerity, but all of our encounters with them have been very smooth - I can't say that we felt the NHS cuts even recently. But I would vote for Tory regardless -
The NHS itself is obviously not private, so you've been experiencing public healthcare, which works fine - when you don't fuck with it. YOU might not feel the NHS cuts, but it's vulnerable patients who definitely do, as do healthcare staff. Patients have to be practically pushed out of hospital in some areas due to the bed shortages. It's easy to brush off the complaints and say "it's not affecting me, so it's obviously not an issue", but when you actually look into it, it has a huge impact on society as a whole. Staff working longer hours and fewer beds available definitely don't have a positive impact on society let me tell you.
As for why no to privatisation of healthcare, well, first of all look at the drug industry. That alone should be enough reason.
The other (more relevant to the average joe) reason is that it would take even more funding away from deprived areas, which already have significantly less invested in them, despite needing it more than well-off areas. That same principle would also be applied to actual procedures, with the ones which you can make money off of being done by private companies, thus taking away extra funds which could otherwise be put back into the healthcare system to subsidise more expensive procedures.