Fatheads full of drink? (4)

I believe the answer is:

mugs

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'fatheads' is the definition.
The definition and answer can be both people as well as being plural nouns.
Maybe there's a link between them I don't understand?

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for mugs that I've seen before include "Gullible people" , "Fools - faces" , "Cups without saucers" , "fools and > grimaces" , "Cups; dupes" .)

I've seen this clue in the Evening Standard.

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