My friend works in IT defence contracting and his stories with the govt pretty much along the same lines. They have no absolutely concept of budgets, efficiencies, or how private business operates.
The solution, in my view, is not to strive for more efficiencies in government; it to strive for less government.
It's not that they have no concept for it - it's worse. It's that they know but won't do anything about it, because the bureaucracy in getting anything changed is crazy. There's no tangible benefit to taking action to change it, because all it does is create more work and they get paid the same regardless. In the private sector, you have targets, profit margins, career advancement - it's not the same in the public sector; all targets are arbitrary numbers like waiting times etc.
The NHS is the sacred entity that can't be criticised or touched, so because of that you see nothing change. A contract agreed in the 90s will persist to this day with auto-renew and price increase clauses, simply because it's the way it's done.
It's the inherent danger in the nationalisation of anything. It is, in theory, a good idea - in practice, it often isn't.