I read the whole article and still don’t know what a cockwomble is.
Pretentious b**t**ds.
If they really wanted you to understand what they were talking about they wouldn't have used an obscure British slang term like "cockwomble".
Cockwombles) (Britain, slang, derogatory) A foolish or obnoxious person."
"https://en.wiktionary.org/wiki/cockwomble"
(Those online dictionaries are handy tools to use whenever you encounter a word you're not familiar with. I've found that Mark Steyn's writings can often be a treasure-trove of new words for me, and I think that's terrific, because it's great to learn new words.)
(For "cockwomble", I at least knew right away that it wasn't the same thing as a "pink-headed warbler".) :-)