There may not exist an objective answer to your question. But we can at least answer the related question: "What are the potential factors that might have caused a decline in the use of 'subjunctives' in English?". Such factors include:
- the fact that whether or not the "ordinary" inflected verb form is used doesn't seem to affect speakers' ability to interpret such verbs as mandatives: for example, if I say "They asked that he left. But he refused.", then, despite the form "he left", we don't perceive a contradiction between the two sentences and we understand that he didn't actually leave.
- the fact that there are alternative constructions, e.g. instead of "They asked that he left", I could say "They asked him to leave".
- differences in how prescriptive English education is in the two countries;
- differences in attitudes towards avoiding "overly elaborate" English in the two countries (see the "Plain English" campaign);
- the fact that the English 'subjunctive' is probably an artificial phenomenon in the first place (in its Modern English manifestation), so more subject to the whims of fashion than other more "core" language phenomena.
Now, one thing to bear in mind is that it's not entirely clear that the premise of the question is true in the first place. In other words, it isn't necessarily true that, in either variety of English, the 'subjunctive' forms have ever been terribly prevalent overall compared to other alternatives. Many commentators have had this impression, and talk about a supposed decline from an imagined golden era when the Modern English 'subjunctive' was prevalent. But it's not clear that actual data bears this out. What may be more the case is that, in both US and UK usage, the 'subjunctive' has had a marginal resurgence recently from a very low starting point, and that in the US that marginal resurgence has been ever so slightly less marginal. But it seems to depend heavily on what data you look at using what measurement methodology. In short, it's difficult to answer your question and pin down concrete triggers for a pattern when it's not clear what that pattern is in the first place.