So Boerd said
In the course of my research on British political heritage, I've just learned from reputable and well-reasoned sources that today there are thousands of frankly ordinary blokes (to say nothing of the hundreds of unimportant nobles higher up) in the line of succession. Therefore, it is not only posssible, but probable that the Dominion found in its early years a legitimate king to exercise monarchial powers, to say nothing of any charlatans showing up with vellum proving descent from Sophia of Hannover.
I wouldn't say 'probable', but I guess it's possible. You do need to consider the Great War wiping out not only a lot of people, but a lot of information too. Most people don't even know what the old United States was like, let alone what some foreign nation may have been like. Hell, most people outside of NCR may not even really understand the concept of nations, or governments beyond simple chieftains and the like. So the average wastelander wouldn't even know a place called the 'United Kingdom' existed, and that it had a monarchy. They wouldn't know of any distant claims, or have any proof to back it. On top of all the widespread destruction and loss of records, you need to add in the fact that a lot of time has passed since the bombs. Enough time for distant claims to have been forgotten, or lost when those making them perished. This is if they survive the bombs at all.
Not to mention the average person isn't dwelling on some super-distant claim they may or may not have, especially considering that no one (besides House, I guess) truly foresaw the bombs. The 'ordinary blokes', as you said, probably weren't expecting to ever become anything more than ordinary people. They weren't sitting around dwelling on these extremely distant claims they may or may not have had, because even if they did had the claim, it would be so distant their chances of ascending to royalty were zero. This stuff probably wasn't in their minds. It'd be a story that, at best, gets told at family reunions and no one takes seriously. Pretty much grandma saying "Did you know our family is in line for the throne?" and everyone giggling because she's grandma and her mind is frail. This makes the likelihood that these 'ordinary blokes' survived the war to make good on their claim very small, since most of them probably wouldn't even know about it, or may have not even taken it serious. Especially if these ordinary people lived in pre-war America, where these claims would have meant even less to their families.
If you were to say that a noble was serving with the Royal Navy and ended up surviving the war, though, then yeah, sure. Everyone on the ship would have known him. His claim would be indisputable and certainly in the noble's mind. It's possible the ship crews supported him and he became king of some radioactive ashes shortly after the ships made landfall. But some ordinary, American wastelander being found, or showing up, to claim some distant claim that his pre-war American family somehow knew about, and for whatever reason saved records of - records which then somehow survived the Great War and were passed down to surviving members of the family - is.. well, not very likely.
So either a noble was aboard one of the ships and was proclaimed king early on because everyone knew of his descent, or some ghoul who used to be royalty/nobility ended up saving up proof of his claim and somehow ended up cashing it in with the sailors stranded in the Americas. If the latter, then he'd either still be king, or died without a biological heir since ghouls can't breed. He may have named someone else king, though, I guess.
