Signalling to leave EU separately? It shows a lot of cheek (1-6)

I believe the answer is:

g-string

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'lot of cheek' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for g-string that I've seen before include "Skimpy loincloth" , "Minimal wear" , "Thong" , "Air on a - -" , "Violin catgut - stripper's garment" .)

I've seen this clue in The Telegraph.

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