I haven't been able to find anything on the Internet to confirm it, but I have a clear recollection of a story about young Brit wastrel saying: "I don't care a fig what the people think, but what will the governor say?" No obscenity involved, just a variant on "don't give a damn".

I finally found this in geocities Brit slang site:
not care/give a fig (for)(v) :not to care at all.