Building regs may well stop you from building exactly the same thing, however I would have thought it would be possible to build something very similar out of similar materials to meet building regs. I would expect to have all sorts of problems proving to building control that it meets the regs but I don't see anything in principle that would rule it out. If the materials used have antiquate strength and insulative properties then it would be fine. The problem would be in proving this.
Actually, getting building regulation approval for earth structures is no big deal. All you do is give them the calculations and... bingo! They used to be prescriptive, but these days as long as you can prove it'll stand up there's no big deal. And, as a rule of thumb, cob is one-third as strong as the equal volume of concrete.
However, while I'm one of the world's biggest fans of cob (and live in a cob cottage) the slightly wacky adobe thing leaves me cold.