Exactly my point!
The NHS and the State shouldn't be paying out anything, we should have a system that covers our liabilities. And if that means people paying some cover fee through taxation then so be it. We can't afford £11.5B at the moment, we have a financial black hole to fill, half of it swallowed up by compensation claims.
I think the NHS has indemnity insurance to cover their employees, as I understand it the indemnity that covers negligence or malpractice where a patient is injured is state backed. There's an argument for that to be covered by the private sector, and like you say, the insurance bill to be covered by taxation. But then would Govt be doing the right thing by paying private insurance when the NHS is already badly underfunded ? And what private insurer would touch it ?
Anyway, I agree it's an eye watering amount to be paying out. But I also agree that those who were affected should be compensated.

