Crafty Cockney's drunk or rolling with it (6)

I believe the answer is:

adroit

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'crafty' is the definition.
(thesaurus)

'cockney's drunk or rolling with it' is the wordplay.
'cockney's drunk' becomes 'ad' (I can't justify this - if you can you should believe this answer much more).
'rolling with' indicates anagramming the letters.
'or' mixed up with 'it' makes 'roit'.
'ad'+'roit'='ADROIT'

Can you help me to learn more?

(Other definitions for adroit that I've seen before include "To raid (anag)" , "handy" , "skill" , "Deft and skilful" , "Quick and clever in action or thought" .)

I've seen this clue in The Telegraph.

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