England's Mythology?

[Lalaith]

All this leads me to wonder - is it in fact possible to draw as many parallels between myth and folk tradition as we are all wont to do? Are they that connected?
Perhaps myth is what Tolkien called " 'high', purged of the gross" - metaphysical questions, the nature of creation, art and knowledge; folk tradition is much more concerned with the basic human requirements: food (lack of or plenty); fidelity (ditto, whether between men and women, brothers-in-arms, or men and beasts), and fighting.
And where do fairy tales fit in? Perhaps most fall into the folk category, although some, like the Cupid & Psyche variants (Beauty and the Beast/East of the Sun West of the Moon etc) might have more mythical elements.
The themes of the Silmarillion tales seem more metaphysical/mythical than folk tradition: Feanor (art and creation) Beren and Luthien (love beyond death) The children of Hurin (fate and despair).