Beer after milk drink good -- hurry (5,1,3)

I believe the answer is:

shake a leg

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'hurry' is the definition.
(thesaurus)

'beer after milk drink good' is the wordplay.
'beer' becomes 'ale' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'milk drink' becomes 'shake' (shake is a kind of drink. I am not sure about the 'milk' bit.**).
'good' becomes 'g' (abbreviation).
'ale' after 'shake' is 'shakeale'.
'shakeale'+'g'='SHAKE A LEG'

Can you help me to learn more?

(Other definitions for shake a leg that I've seen before include "Hurry up" , "Get up - be productive" , "Get a move on" .)

I've seen this clue in The Telegraph.

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