We have privatised medicine for those that want and can afford it already. Privatising won't improve what we have, letting local NHS employ the staff directly may. Looking at the industries this country has privatised so far, it's only led to profits for the rich, not improved the service and, rail for example, has made things more expensive and worse, making profits whilst still getting tax payer funding, which is a joke. We need to move away from filling these greedy shits pockets and, I reiterate, housing, health and education should not be for profit.
Are you incapable of seeing shades of grey, is it for you either privatised 100% or 100% nationalised? Most of Europe have significant chunks of their healthcare system privatised, this doesn't mean that the citizens have a worse level of care, in fact in almost all cases its better than the UK with shorter waiting times easier access to specialists etc.
I think the entire NHS needs a radical rethink on how it can become more efficient and serve patients even better.