Well I must admit I was taken aback the first time I was told that I was a "bit cheeky".
Anyway, there is a connection between the word fag meaning a cigarette and fag being a derogatory term for homosexual.
A fag in its older usage meant a glowing ember. Back when burning at the stake was a common way of ending a person's life, it was deemed a waste of a good firewood to burn a homosexual. Therefore, homosexuals were tossed on the dying coals thereby tossing them onto the fags. Therefore the derogatory term.
which ties into the origin of the word in its full term: "faggot" which is a load of firewood.
