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?

closed as off-topic by Jason Bassford, curiousdannii, jimm101, choster, Chenmunka Feb 27 at 18:27

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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.

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