Why is “a” used before “smoke” in this sentence?

I only have half an hour-barely time for a smoke and a cup of
tea.

Smoke is uncountable so why is there an article used?

Answer

In this case, “a smoke” is a cigarette. “Have a smoke” means go out and have a cigarette.

6a(1) : something (such as a cigarette) to smoke

You are correct that some other meanings, such as the stuff that rises from a fire, are uncountable nouns.

Attribution
Source : Link , Question Author : 41Games , Answer Author : Damila