LOL! It is fascinating.
From what I understand, the contemporary meaning of 'fag' is a cigarette. It's derived from the older word 'faggot' which was a tightly wrapped bundle of sticks used by people who were too poor to purchase real logs.
Yes, that’s what they call (or called) a cigarette. I remember the days when you could ride the tube and see guys rolling and lighting up their...tobacco cigarettes. Those days gone forever. I can’t find any smokers in London anymore!