The term 'fag end' predates the cigarette by a couple centuries, at least in Europe. In figurative use, I am surprised to see it associated with cigarette butts; it's a very unusual figure, and I would have expected anyone using it to be aware of the (original) meaning.
I would be greatly surprised if more than 1% of UK respondants had any idea of the use of "fag end" as anything other than cigarettes and the metaphor.
Sorry, I should have mentioned. For anyone else reading, "fag end" refers to the end of a length of material such as cloth or especially rope. The short end of a rope which is left over from tying a knot is the "fag end". Another similar term is "bitter end", the end of a rope abaft the bitts, that is, the part that remains inboard on a ship.
