So you're not counting Scotland and Wales then, just England? Because Britain's borders have changed a lot over the centuries...
Anyway, according to your rules no English king has ever been legitimate. Rome rules over Britain and they certainly had a more than enough development in their empire. Heck, after the borders of Rome changed and retreated to East the level of bureaucracy in Europe collapsed and it took centuries until another nation had a bureaucracy that could control an area bigger than a city.
And as I've said before, the Byzantine empire was a direct continuation of Rome (despite your bullshit claims otherwise) and therefore the inheritance of England went to Byzantine (whom the English and other European nations attacked unlawfully) and then the Tsar and finally Finland after the collapse of Tsarist Russia. The first and only king of Finland still has descendants in Germany if you want to find them and put them on the throne of England.
(And if you're going to go for some other bullshit excuse again I'll remind you that if a nation collapsing means that the new ownership goes to some other country rather than the heir then the current queen of England is the rightful ruler because her family got the throne and therefore the previous line ceased to be the rightful rulers.)