England isn’t big enough for so many different types of labels. In America, there are enough of each type to give it a name, find themselves some Rabbanim, open Yeshivos tailor made to their needs. In London, there are not that many high schools. For boys, there are two Yeshivish/Heimish schools [Pardes House and Beis Hamedrash Elyon], another one which less Heimish, less Yeshivish, more anglicised and is a matter of opinion whether it is as Frum [Menorah Grammar], and then one school which is the closest England has to Modern Orthodox and plenty of people in the school don’t keep Shabbos [Hasmonean]. (From what I understand, there are differrent sections in the school for different levels of Yiddishkeit, ranging from non-existent to above average.)
Although we have all different types of Yidden here, they are labelled a lot less. Another point is, because we don’t have the numbers, everyone is forced into some level of conformity one way or the other. Having bigger numbers justifies people to live the way they want.
There are definitely people like you mentioned. (Of course, the description was slightly vague and can apply to different levels, but we have those levels too.)