Just some thoughts for your friend

'Tolkien creating myth for us poor impoverished Brits.'

Actually Tolkien wanted to create a mythology for the English, whose own mythology had been largely lost.  The Mabinogion was based on Celtic British, in particular Welsh, mythology, and the whole Arthurian mythos and the 'Matter of Britain', was British mythology, created I think by a fusion of surviving Celtic British stories with those of Bretons coming 'back' to England with the Norman invasion, with a French slant on them (for example in the stories related by Wace and Layamon).  Beowulf is about the only large scale work to come down from pre-Norman England, and it's survival was purely by chance.  From the 16th century until the early 1800's it survived as a single manuscript, which was almost lost in a fire (the edges of the manuscript were in fact burned).  The Eddas were from the related but not identical Norse mythology, and only give an idea of what might have been present in the old English system.  I'd recommend the 'Lost Gods of England' by Brian Branston for a good look at what this might have been and as a comparison with the Norse and German systems.

To return to the Arthurian myth and the related Grail stories, I think they are a great myth for Britain, and I don't really agree with Tolkien's objections to them (though I think these are often rather overstated by some people).  It does have very deep roots if you look for them, probably back to the pre-Celtic people of Britain, but then again a lot of the stuff in Lord of the Rings does as well, as Tolkien 'imported' lots of surviving fragment of English and other myths into it, as well as creating a strong story with Archetypal figures that reflect 20th century ideas.  In that way I think he builds a bridge between these ancient things and the modern world, which may not always work with the Arthurian myths.  Then again the Arthurian stories work better at other things, and personally I wouldn't be without either.  It does of course depend on which Arthurian stories you mean, Mallory, Tennison, T.H.White, Mary Stewart, the various 'true' or 'real' Arthurs written about recently.  They all reflect the Arthurian myths, but in different ways.

'It's coming to the moviescreen well - but in a 10 hour chunk - and even that sacrifices a lot of detail.'

I'd agree here, but then compare film adaptations of the Arthurian myths.  The best I can recall is Excalibur, which crams the whole lot into 2 hours.  I've often since thought that it does to the Arthurian stories what the single film version that some film companies wanted for Lord of the Rings. 

'King Arthur we can assume an awful lot about the background of the story, whereas Tolkien specifically gives us the information about almost everything - languages, peoples, maps, prehistory'

Yes and no here.  Tolkien does give a lot of information if you consider just The Lord of the Rings.  However, looking at his whole mythology there are large areas of haziness.  For example not that much is really known about the history of the Second Age, the more Eastern and Southern regions of Middle-earth where Numenor it appears had colonies, the histories of Arnor and it's successors (I could go on and on here).  To compare this with the Arthurian myths, we know very roughly the history of the end of Rome in Britain, and the names of some of the successor Kingdoms, others such as Calchfynedd only survive as names, (this story I've always thought reminiscent of the breakup of Arnor in Tolkien's Middle-earth).  So we know the maps, peoples etc for the historical Arthurian stories as well.  Of course that's only the 'top' layer, but the Lord of the Ring's is in a sense only the 'top' layer of Tolkien's mythology as well.  Finally;

"And do the parts separate as well as the Tales of the Knights of the Round Table"

Depends on which parts you mean.  The Lord of the Rings is an indivisible unit in Tolkien's mythology, but stands alone, though it's related to, the story of Beren and Luthien and the other stories outlined in the Silmarillion.  To conclude, I'd say that, considered on it's own, the Lord of the Ring's doesn't work entirely as a myth, but in its wider relation to the stories of the Silmarillion etc, which is how it was designed, it works very well indeed, which is of course why so many people feel so powerfully drawn to it.  It is these half glimpsed stories, of Gil-galad, Beren, Numenor etc, that give Lord of the Ring's its depth.