I dread the scenario where the hospital, or even before that, the paramedics check to see how much you can afford before care begins. Of course those who can afford private health care aren't going to be worried, unless they give a fig about the less well off.
Hospitals are using agency nurses at great cost. I know a nurse who works in a hospital and also works overtime for an agency at the same hospital for a high fee. Multiply that by however many nurses are employed in this way and I'm guessing it's a huge amount.
A friend has been confined to a care home post op because there were no carers to visit her at home. When it went beyond the 6 week limit free care, she wasn't charged because, 'it wasn't her fault'. That continued for 4 weeks. She's home this week and an emergency care team from social services are making 4 visits per day free of charge because they still haven't got a care team, so she can't have a care package contract. It seems a shortage of staff is the main cause of this particular drain on the NHS.