This seems like such a broad statement that it can't be accurate. I'm assuming you're referring to some non-emergent and elective procedures, right?
> But the new rules, drawn up by clinical commissioning groups (CCGs) in Hertfordshire, say that obese patients “will not get non-urgent surgery until they reduce their weight” at all, unless the circumstances are exceptional.
And what is "non-urgent surgery"? Who knows. If you need knee surgery, it's probably not urgent, but you may not be able to work without it, thus having very high social costs (unemployment, disability benefits, lost labor, ...) as well as very high personal costs. But NHS almost certainly doesn't have the resources even to consider the negative externalities of this policy -- they are acting out of desperation.
In the UK right now you cannot get surgeries from the NHS if you're a smoker or overweight. They've already made the leap you wonder about.
And there's been talk of the same thing in the U.S. for Medicare.
When you have access to private healthcare, you can decide where you draw the line (based on many many factors, including what resources you have, what resources you want to pass on to your children, etc.). When you don't, you're at the mercy of the state.