Well, it seems to me that there is some kind of concensus here that the description of Tolkien's work as Edwardian is flawed.
A good thing, too, as most paradigms are limiting. Also, to see his work in light of the Edwardian values concerning the upper classes would, I think, prompt the tendency to see the elves as members of an aristocratice class that had little interest in other denizens of Middle earth and which was shortly to be swept away by the rising hoards of workers, aka the hobbits and men. Not something that I think Tolkien had in mind.
As for the "Englishness of English art", might I humbly suggest
Peter Ackroyd's Albion: The Origin of the English Imagination , particularly for his sense of English spirituality, as opposed to "preaching," to say nothing of themes such as tree and garden, stone, the sea, melancoly, ruins and sublime. I think there is much more Tolkien to be found in these themes than in the minutiae of daily life. To
davem's observations about Chaucer's audience, let me add that Chaucer's characterisation of his Wife of Bath, for instance, owes much to medieval stereotypes of the cuckolded husband--literary caricatures rather than any known historical personage.
This is some ways away from Edwardian literature, but perhaps something can be found in Lobdell's theory concerning the relationships of boys and men, an aspect which Tolkien would have found in both his ancient sagas and Edwardian literature.