Isn't that family mostly German, or from thereabouts, anyway? If the British want a king or a royal family, as a symbol or something, maybe they could track down people who descend from some of the older and more purely British royalty? If they got a king, or a queen, who had not been born into that position but had lived among them as one of them at least he might "get" his people a bit better. The position of a monarch in any country is legally mostly just symbolic these days anyway, they don't have much in the way of official power, what power they do have is all sort of "under the table" kind of thing, connections etc (besides lots of money).

Symbols can be kind of important. But you need ones that work for you, not against you.