Heh, I'd have to consult my books (/Giles) but it is possible that Tolkien considered Norse and Germanic influence to be British enough to include. I know he intentionally excluded French and American elements (thus what was "tobacco" in The Hobbit became "pipeweed" in LotR - "tobacco" being an American word).

So it is possible that you could argue that LotR isn't technically Anglo-Saxon in the strictest definition. It was intended to be very, very British (or maybe very, very English), though.