In reply to Keith Tanner :
Ran into the same thing when I had a house in the UK while living in the US. Made for a fun tax return, especially as the tax years don't fully align.
As my client today seems to want me to be on call, I can elaborate on a few things.
The comments re the health system are something I can pretty much confirm after having experience with the German system, the UK one and the US one. The German one isn't really single payer but people are required by law to have health insurance from an approves provider. It's not as expensive as over here, but coverages have been cut for decades. The social safety net has also been eroded somewhat, and that can lead to funny choices - my cousin and her other half have been together well over a decade, own a house together and all that, but refuse to get married as that would make them responsible for care cost for each other's parents. The other half went through this with his mother and it nearly financially killed him to the extent that he can't afford to go through this again. And other parts of the safety net now have a lot of holes in them as well.
The UK system mostly works as designed - emergency stuff tends to get dealt with quickly, the other care has to wait. It's going a bit downhill though with frequent funding cuts and now with Brexit (the UK employs a large number of EU and non-EU personnel in the health care sector). The rest of the safety net is also not that great and like in Germany, my generation isn't sure if it'll be around until we retire. But at least the UK doesn't take a huge chunk out of one's paycheck for the state pension system and tell you at the same time that you probably won't get much or anything back out.
The one emergency-ish I had in the UK was dealt with in the same quick manner I would have expected from the system in Germany. I had been suffering from what my GP (family doctor) thought were bruised ribs, but they weren't healing. It also felt link there was a lump under the ribcage. I think I got to about the 'p' in lump before he had his receptionist call the local hospital for the required tests, which started within a week or so, followed by about six months of monitoring. I did have an out of pocket cost for some of this (a pound or two for parking at a hospital further away).
The 'not from here' kinda has been following me around since birth, so I never really noticed it that much. The area in Germany I was born and grew up in has a strong regional dialect, and my family moved down there from northern Germany after the war. So I grew up not speaking the local dialect, which immediately marked me as "not from here". But yes, I got the occasional question about where I'm from in the UK and the US - I don't really have that strong a German accent so a lot of people in the UK thought I was from Norway or Sweden, with a bit of South Africa thrown in. In the US, people either think I'm from a funny part of Britain or if they have been to Germany, often correctly guess Germany.
The credit history thing is an interesting one. As Keith wrote, it doesn't follow you from country to country, not even in the EU (at least back then). However the credit history and score seem a lot more important in the US that they are in Europe. in Europe you obviously run into issues when you want to borrow money and have no or bad credit, but it doesn't make your car insurance rates explode and potentially cost you a job like over here.
In the UK I mainly lived in the Southeast where people are used to immigrants and did have few problems there - other than the border guards asking me every time if I was going home (with an implied "finally") every time I went on a European vacation. Friends of mine from Eastern Europe didn't necessarily have the same good experience.
In the US, I think the combination of everybody being from someplace (and often "someplace else") and being at least the right shade of pale has generally have me fly mostly under the radar. I got the "coming here to steal our jobs and women" once or twice in the fifteen years since I've been regularly traveling over here and hte eight years I've been a permanent resident. Living in Nevada where it's not always considered polite to ask people where they are from (and in some cases in the backcountry, potentially hazardous to one's health) can be a factor in this, though.
I'm also a bit of an in-betweener like Adrian mentioned. I can't see myself going back to Germany for a lot of reasons (and that's before I'd even look at much lower salaries and higher taxes there) and I've not felt "at home" there for a long time. I might get more German the further I get away from there, but I'm not when I'm there.
I felt a lot more at home in the UK than I did in Germany, and now the same feeling is slowly developing in the US. I'm not a citizen yet, but I'll probably be in a few years. We haven't quite found the right place to live for us yet anyway, so we'll be trying the East Coast for a while, and the area (NoVa/WV) reminds me very much of the area in Britain I used to live in. Right down to that dang rain.