Wit coming from British weather authority (10)

I believe the answer is:

brainpower

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'wit' is the definition.
(I know that wit can be written as brainpower)

'british weather authority' is the wordplay.
'british weather' becomes 'brain' (I can't justify this - if you can you should give a lot more credence to this answer).
'authority' becomes 'power' (I've seen this in another clue).
'brain'+'power'='BRAINPOWER'

'coming from' acts as a link.

Can you help me to learn more?

(Another definition for brainpower that I've seen is " intelligence".)

I've seen this clue in The Independent.

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