Crossword Genius

One who demonstrates British saying (7)

Ross

I believe the answer is:

proverb

I'm a little stuck... Click here to teach me more about this clue!

'saying' is the definition.
(I know that proverb is a type of saying)

'one who demonstrates british' is the wordplay.
I cannot quite understand how this works, but
'british' could be 'b' (abbreviation e.g. in 'BBC') and 'b' is found within the answer.
The remaining letters 'prover' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for proverb that I've seen before include "Traditional saying" , "Adage, pithy saying" , "'Adage, saw (7)'" , "Familiar saying" , "Old saying, perhaps by Solomon?" .)

I've seen this clue in The Times.
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