Privatization has always been an incredibly overloaded term when it comes to the NHS. No party is proposing getting rid of state healthcare. The left wing argument against markets in general even interacting with the NHS is usually along the lines of [I don't want those fat cats profiting off peoples health]. This makes me wonder: As long as the care is universal and free, who cares how it's delivered.
I feel the best pro-"privatisation" argument is found in the Liberal Democrat Orange Book.
The left-wing argument is that businesses exist to maximise profit, so once you have the profit motive involved it'll eventually have to be paid for at point of use or not have it at all (assuming public funding is denuded).
This is a much of an article of faith as the right-wing argument that the profit motive means costs will go down and governments won't have to pay very much.
Both ends of the spectrum are ideological fantasies of course, but the NHS is caught in the middle.
I feel the best pro-"privatisation" argument is found in the Liberal Democrat Orange Book.