I didn't see that (or any of his) episode, but I have to wonder why one would want a cotton tarp. Thin cotton would leak like a sieve, cotton duck would be super heavy.
Campmor (campmor.com) has a waterproof tarp 10ftx10ft of "coated high count taffeta nylon" that has 21 tie tapes on it, you can tie it in a variety of positions. It weights 38 ounces, which isn't the lightest in the world, but I have had one for about 15 years, and it is still going strong. Go to their website and do a search for tarp to see it and all of their others. Not sure if they ship across the pond.
They also have several silnylon tarps that weight about half as much, but cost almost three times as much...