There is a dialect word cobb. I have heard it used round here, not just in Birmingham, as in "don't speak to him, he's got a right cobb on". This usually means they are in a bad mood rather than feigning illness though.
http://www.thedialectdictionary.com/view/letter/Brummie/2163/
I only remember it on this thread, dannyk, but the suggestion of COBB seemed to be tentative and there were no links to substantiate it. Maybe there was another thread. Do we know which crossword it was?
I've done a n AB search can't find any other threads where cobb was the answer other than one asking for a gull, although I did learn that Ed Cobb wrote Tainted Love.