The state will not provide it to non-residents. As soon as you arrive in the UK, immigration stamps "no recourse to public funds" in black all-caps into your passport as a friendly reminder.
In this specific instance, you're probably right that there will be paperwork.
However, in general, acute healthcare in free in the UK and does not even require ID. I don't know if that's how it's "meant" to be, but that's how it is; if you're on vacation in the UK and something bad happens, you can just turn up at the nearest hospital and it will get sorted out, no bill no fuss.
Foreign nationals without a visa (and non-resident British people, like me now) do receive a bill. I used to work in the department that recovers the money.
Out of curiosity, what kind of money we are talking about? For example checking up sprained ankle at A&E?
Many of my friends being disappointed with NHS go for example to Mexico for private treatment and it works much better that doing it here, plus you can enjoy the climate and great food.
Not giving medical advice but you probably shouldn't be going to A&E for a sprained ankle unless it's very serious or a suspected break.
For people who are not ordinarily resident in the UK an A&E admission costs £100-£500 plus any tests and treatment. There's a small amount of margin which is used to offset the cost of recovering the money and the fact that sometimes the bills go unpaid.
I see, so it is not the kind of situation when you need to consider getting mortgage to pay off the medical bill.
It was just an example. General advice I heard is that when you can't go to GP and walk-in is either too far away or closed, you can go to A&E or call 111 for instructions.
It's not like the US system where people have to choose whether or not to call an ambulance but it's obviously better for visitors to come with health insurance since a policy covering most emergency healthcare, and various other eventualities that could happen on a trip, is probably around US$10-20 pp.
Yeah most of the NHS hospitals I know have "Minor Injury Units" - I generally think that if you can make your own way there they it probably isn't one for A&E.
Mind you the last time I went for something I thought wasn't very serious (a cat bite) I was told to go to A&E pretty quickly!
How it’s “meant” to be is that you’re asked for where you’re registered, and your NHS records are pulled up, and if you’re not registered at a GP practice or in the NHS system you get a bill
That's not the case. There's no such thing as a single NHS records system. There's 4 separate NHS systems for each constituent country of the UK. If you go to A&E they cannot generally see your GP records - if they can, it's usually limited so for e.g. if you live in the same local NHS trust as the hospital is in.
If you aren't registered with a GP and have no records at the hospital there are other ways to check, for instance your National Insurance records. It's not easy to get away without paying if you are an ineligible person.
But I think there are some exceptions for communicable diseases, which they will treat without attempting to bill you. I doubt vaccination would fall under that but don't really know.
I think doctors have to ask for ID if they suspect someone is not eligible for free treatment. I know this happened for two of my friends and they had to show ID at A&E, but that was during the heat of Brexit campaign, so this could make doctors feel encouraged to do such checks. I have not heard about it for a long time now though.