Malcolm, I used to rep for a dealer of these types of products. "Starboard" is one brand, "Designboard" is another. They are all HDPE plastic, which machines easily but as you noted, is soft and needs to be at least 3/4" thick in order to have any sort of structural rigidity. Also, HDPE distorts and gets soft in the sun. Typically, you clad something with it. There is a rubberized acrylic made by Chemcast of Mexico that is actually designed to be drilled for Blum-type hinges and grabs screws but it is quite expensive. You might also check out Corian or one of the other acrylicized solid surface materials. I had several clients who used them for outdoor kitchens. Good luck in your search.
Erik