Backwoodsgirl, you're on the other thread bragging that you wouldn't dream of moving back to the UK, and that living in the US gives you the kind of lifestyle you'd need a lottery win for here.
Nice to see you do, in fact, acknowledge that your position is more precarious than it seems. Job loss? Long term chronic illness? Cancellation of your (extremely cheap for the US and probably for a reason) health insurance? No problem: you've fraudulently maintained a UK address for NHS access, even though you're not ordinarily resident here and definitely not entitled to it.
Funnily enough, you didn't mention this when explaining how awesome your life in the US is. I can't stand this kind of expat: shameless boasting about your new life and how you'll never be back... but quietly expecting to sponge off the NHS if you ever need it.
OP: I was six months pregnant when I moved back to the UK. I was able to register with a GP and access treatment there without issue, but I couldn't properly book in to or receive antenatal care at the local hospital until I proved I had relocated here permanently. This involved showing a copy of our rental contract and DH's work contract. I have a British passport and had been overseas 5 years.
Some hospitals have very efficient departments dealing with billing and international patients, and some are completely clueless, so you'll hear about a range of experiences.