If I'm understanding this correctly apparently Tolkien believed we don't have some Saxon equivalent of Norse mythology is that Normans weren't interested in preserving Saxon culture.
ETA: I thought OP was asking about Tolkien. So that's what I wrote about.
This House deplores the occurrence of the Norman conquest.
-debate topic proposed by Tolkien in high school
Despite basing his first conlang (constructed language) on French, which he spoke fluently, Tolkien later grew into a deep distate for France, French, and French food. Critics have long noted the lack of French literary and philological influence in LOTR and its surrounding texts--especially striking, the lack of references to the Anglo-Norman/French-steeped Arthurian tradition. And when Tolkien catalogued the long history of popular and scholarly crimes against his beloved Beowulf, the French came in for targeted criticism:
We must pass in rapid flight over the heads of many decades of critics...Beowulf is a half-baked native epic the development of which was killed by Latin learning; it was inspired by emulation of Virgil, and is a product of the education that came in with Christianity; it is feeble and incompetent as a narrative; it is the confused product of a committee of muddle-headed and probably beer-bemused Anglo-Saxons (this is a Gallic voice); it is a work of genius, rare and surprising in the period, though the genius seems to have been shown principally in doing something much better left undone...
So when Tolkien wrote to an unidentified reader in 1956:
The task...being precisely to restore to the English a mythology of their own
it's easy to see him blaming the French for the erasure of a true English mythos. But the inability of post-Norman English literature to satisfy his burning desire for the world of Faerie, or the "Perilous Realm", and for an English mythology to parallel especially the Finnish tales he had grown up reading, ran deeper than simple Francophobia.
Scholars across northern Europe had spent the 19th century rekindling their linguistic-national epics and legends, a body of work and literature that Tolkien was very familiar with. So he saw the loss of English mythology as part of a wider trend. Referring to the reconstruction of the Finnish poem Kalevala, he argued:
These mythological ballads are full of that very primitive undergrowth that the literature of Europe has on the whole been steadily cutting and reducing for many centuries...I would that we had more of it left.
In one of his two most famous lectures, "On Fairy-Stories," Tolkien elaborated on the loss to folklore, especially the world of Faerie (Tolkien considered the fairy world, not fairies themselves, the primary marker, significance, and lure of fairy-stories).
As for diminutive size: I do not deny that the notion is a leading one in modern use [but was not always]...The diminuitive being, elf or fairy, is (I guess) in England largely a sophisticated product of literary fancy. It is perhaps not unnatural that in England, the land where the love of the delicate and fine has often reappeared in art, fancy should in this matter turn towards the dainty and diminutive, as in France it went to court and put on powder and diamonds.
Tolkien gets in a jab at France, and the historian can't help but think of how it's precisely the elite culture of England and France that overlapped and melded and succumbed after 1066. But for Tolkien, the degredation of Faerie and mythology is, again, a broader matter:
Yet I suspect that this flower-and-butterfly minuteness was also a product of 'rationalization,' which transformed the glamour of Elfland into mere finesse, and invisibility into a fragility that could hide in a cowslip or shrink behind a blade of grass. It seems to become fashionable soon after the great voyages had begun to make the world seem too narrow to hold both men and elves.
Tolkien was famously insistent that LOTR was an allegory for nothing, a metaphor for nothing, but it's easy to see how critics, fans, and filmmakers have read critiques of modernity into certain aspects of his books.
But as we will see, there was one more element that Tolkien explicitly blamed for the lack of an English mythology--although as always, the French will have their hands in things first. Tolkien, like so many others, was quite conscious that the Arthurian saga had come to play the role of the English national epic, foundation myth, nationalist/patriotic heart. And when Tolkien handled Arthurian material, as he did with nimble philological dexterity (and occasional polemical sledgehammer), his distaste for the French corruption of English language-literary tradition certainly shone through.
The unrhyming, rhythmic alliteration that is found in Old English poetry and peters out after the Norman Conquest (in favor of meter and rhyme) suddenly bursts back onto the scene in the 14th century, although this "alliterative revival" did not last long. Along with several contemporaries, Tolkien viewed the alliterative revival as a deliberate attempt by those poets to connect with the Old English past. This was part of the reason he chose to translate Sir Gawain and the Green Knight, although the very strong Perilous Realm vibe of that particular entry in the Arthurian canon also drew him to the poem.
Later, Tolkien's one original take on the saga, "The Fall of Arthur," used a stripped-down version of Malory's Morte d'Arthur as the framework to update Old English literary techniques and verse forms into modern English. He sought to bring the pre-Norman traditions not just to post-Norman literature but to modern English itself.
But despite his use of Arthuriana, Tolkien believed it could not possibly satisfy the desire ("desire" is his word for the yearning for Faerie) for an English mythology for a fundamental reason: Christianity.
Of course there was and is all the Arthurian world, but powerful as it is, it is imperfectly naturalized, associated with the soil of Britain but not with English; and does not replace what I felt to be missing...It is involved in, and explicitly contains, the Christian religion.
Now, Tolkien declared repeatedly that he was a Christian and even argued for reading the Gospels as a fairy-story in their own right, in their own original time of writing. But to him, the intrusion of Christianity-the-religion into mythology was a catastrophic sin.
Myth and fairy-story must reflect and contain in solution elements of moral and religious truth (or error), but not explicit, not in the known form of the primary 'real' world.
For Tolkien, the power of mythology was that the power and presence of Faerie explicitly highlighted and championed the mundane world, the world of men. He loved Beowulf because, while the world of Christianity had already been to change the minds of men and cast the world into darker (his word) relief, "the shift [was] not yet complete":
Its author is still primarily concerned with man on earth, rehandling in a new perspective an ancient theme: that man, and all men, and all their works shall die...The worth of defeated valour is deeply felt. As the poet looks back into the past, he sees that all glory (or as we might say 'culture' or 'civilization') ends in night.
~~
Cited lectures: "On Fairy-Stories" (PDF); "Beowulf: The Monsters and the Critics" (PDF); other excerpts taken from Carpenter, ed., The Letters of J.R.R. Tolkien
If you'd like some excellent folklore and mythos from GB/Ireland, I highly suggest looking into Thomas Keightley. In particular The World Guide to Gnomes, Fairies, Elves, and Other Little People. It brilliantly breaks down popular folklore down by country/region and has several examples from Great Britain and Celtic mythology. Tolkien is said to have been influenced by Keightley, and an excellent example can be found in the chapter on "Eddas and Sagas"