Me too. I hadn't heard the English-mythology angle (sounds plausible too.) But I remember from a class on CS Lewis learning that both Lewis and Tolkien were both fascinated by & saturated in Norse mythology. Before anyone claims that Tolkien immersed himself in this area because he was an "occultist," let me point out that it was his *job* - he was a specialist in ancient European languages and of course was deeply familiar with their literature, folklore, and mythology.
In fact, that's what makes the story so good, and what I liked about the second Jackson film in particular. The Norse gods die individually; thus the five-handkerchief story of the murdered god Baldur. Love relationships don't really work out well in Norse mythology, and Jackson gave us a little hint of the end of Aragorn & Arwen (again, a 3-handkerchief tear jerker.)
Finally, the Norse gods know that they will die at the end of their history, in the final battle of Ragnarok. They know their tragic end is coming, yet they fight on in a battle against the giants, werewolves, other assorted evil guys *anyway.* The Two Towers are definitely suffused with that dark Norse sadness, even though the story (like Christianity itself) ultimately does have a happy ending.