Middle Earth is most definitely supposed to be the real world. It originated to fill in the gaps in some legends, and establish common ground between them. Even shortly before the time LoTR was written, the primary legendarium (i.e. Silmarillion) had the British Isles formed from the breaking of Beleriand. AElfwine, who was told the Lost Tales, and who survived well into the 1950s (at least) (see the final Ainulindale, for example) was English. And this is not even counting the various definitive statements in Letters (which I don't have to hand and therefore can't directly quote at the moment).