I know that at least at one point, Tolkien wanted his tales about Arda to be a sort of English mythology. However, I think that in Return of the Shadow it suggested that he eventually gave up trying to do this. Since that book was such a large infodump, I may be remembering wrong, and I can't find anything to suggest this online.
I don't recall anything from Return of the Shadow, but Tolkien admitted to giving up on his "mythological history of England" in Letter 131 (emphasis mine):
[O]nce upon a time (my crest has long since fallen) I had a mind to make a body of more or less connected legend, ranging from the large and cosmogonic, to the level of romantic fairy-story-the larger founded on the lesser in contact with the earth, the lesser drawing splendour from the vast backcloths – which I could dedicate simply to: to England; to my country. It should possess the tone and quality that I desired, somewhat cool and clear, be redolent of our 'air' (the clime and soil of the North West, meaning Britain and the hither parts of Europe: not Italy or the Aegean, still less the East), and, while possessing (if I could achieve it) the fair elusive beauty that some call Celtic (though it is rarely found in genuine ancient Celtic things), it should be 'high', purged of the gross, and fit for the more adult mind of a land long now steeped in poetry. I would draw some of the great tales in fullness, and leave many only placed in the scheme, and sketched. The cycles should be linked to a majestic whole, and yet leave scope for other minds and hands, wielding paint and music and drama. Absurd.
The Letters of J.R.R. Tolkien 131: To Milton Waldman. 1951
Reading his early drafts, you can see this English connection, and see it slowly fade away with time; Christopher Tolkien notes this himself on a couple of occasions:
In his earliest writings the mythology was anchored in the ancient legendary history of England; and more than that, it was peculiarly associated with certain places in England.
History of Middle-earth I The Book of Lost Tales, Part One Chapter 1: "The Cottage of Lost Play"
I have shown, convincingly as I hope, the curious and complex way in which my father's vision of the significance of Tol Eressea changed. When he jotted down the synopsis, the idea of the mariner's voyage to the Island of the Elves was of course already present; but he journeyed out of the East and the Lonely Isle of his seeking was -- England (though not yet the land of the English and not yet lying in the seas where England lies). When later the entire concept was shifted, England, as 'Luthany' or 'Luthien', remained preeminently the Elvish land; and Tol Eressea, with its meads and coppices, its rooks' nests in the elm-trees of Alalminore, seemed to the English mariner to be remade in the likeness of his own land, which the Elves had lost at the coming of Men: for it was indeed a re-embodiment of Elvish Luthany far over the sea. All this was to fall away afterwards from the developing mythology; but AElfwine left many marks on its pages before he too finally disappeared.
The History of Middle-earth II The Book of Lost Tales, Part Two Chapter 6: "The History of Eriol or Ælfwine and the End of the Tales"
Although there are certainly elements of this goal present in the later drafts of the Legendarium, the direct references to England and English ideas was dropped; one of the places we see this most clearly is in the diminishment of Eriol/Ælfwine as a framing device, something I've talked about before.
In The Book of Lost Tales, Eriol was a 5th-century Saxon explorer who stumbled across the island of Tol Eressëa, where he learned the history of "Luthany" (ancient England) from the Elvish inhabitants there. Later revisions replaced Eriol with Ælfwine, an 11th-century Anglo-Saxon who does basically the same thing, though he returns to England and translates the lore into Anglo-Saxon, explaining how Tolkien "recovered" it in-universe.
As I've discussed before, the prominence of Eriol/Ælfwine diminished greatly over the history of the Legendarium, with some (including Christopher Tolkien) arguing that he eventually had more-or-less abandoned it.