Except that's not the case at all.

The NHS is underfunded, sure, but in an emergency situation (you know, the kind that will bankrupt you in the US) you won't get treated privately, it will be done on the NHS. Sure, if you have cancer your Chemo will be given in nicer surroundings, but it's the same drugs administered under the same protocol.

All private insurance in the UK gives you is that - a nicer environment and quicker access to treatment for non life-threatening conditions.