The British in Tolkien's mythos were always the humans. He "translated" their speech as English or Old English, so it was quite clear he saw them as Anglo-Saxons. The "British Empire" in Tolkien's world is Numeanor, which made its colonies throughout the world with its great sea fleet, just like the British Empire did, and brought education to "lesser men" (There was always a bit of "white man's burden" in Tolkien, I'm afraid) just like the British claimed to do in Africa and India. Tolkien probably saw the destruction of Numeanor as a warning to the then mighty British that nothing lasts forever, and that power corrupts. How right he was.

As for the Elves, their decline is representative of a far older cultural fading; the loss of the Island of Britain in the Dark Ages by the earlier Celtic people (represented by the pseudo-Welsh speaking Elves) to the Germanic English (represented by the Old English speaking pseudo-Viking/Norman humans). Tolkien, like many people today believed the myth that the Celts were tree-hugging nature lovers who took care of the environment (indeed he could be credited with keeping this myth alive) and depicted the Elves that way