Ah, the 1940's, when ties were no more expensive than a soda is now. I've found a number of early Wembley ties made from silk, linen and wool. I've also discovered a bunch of later Wembleys made of acrylic, polyester and acetate. Fortunately, the company is back at it with a line at JCP, and these ties are once again constructed of natural fibers. Inspired by old collections, the new ties are slim but not skinny and feature simple stripes, plaids, and motifs. Check them out, you might be pleasantly surprised.
Also while you're at JCP, check out the Happy Socks collection.