Carl Hostetter spotted this on eBay and passed on the link in case anyone is interested (perhaps not to buy at that price, but the letter and signature are fully legible in the pictures provided so you can read and enjoy it.) Neither he nor I am affiliated with the seller.

A quote from the letter:
"I am personally averse to dramatizations of my work, especially of The Lord of the Rings, which is too long for reproduction without severe cutting and editings: in my view destructive, or at best severely damaging to a complicated but closely-woven story."