Aside from the offensive meaning, colloquial British English uses the term fag to indicate a cigarette.
James has gone outside for a fag
In my googling, I thought perhaps this originates from one of the possible meanings of faggot:
a bundle of sticks, twigs, or branches bound together and used as fuel, a fascine, a torch, etc.
In a very loose sense, this definition could be applied to a cigarette. It's a collection of materials (tar, tobacco, etc) bound together for burning.
The origin from Etymonline indicates:
1888, probably from fag "loose piece, last remnant of cloth" (late 14c., as in fag-end "extreme end, loose piece," 1610s)
This appears to be speculative, and doesn't necessarily explain why this definition fell into common usage to indicate a cigarette. I'm looking for something more concrete indicating what caused it to be used in this context.
What is the origin of this meaning of the word?