Being drunk, messes up a teach-in (5,3)

I believe the answer is:

china tea

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'being drunk messes' is the definition.
I know nothing about this answer so I cannot tell whether this works.

'up a teach-in' is the wordplay.
'up' is an anagram indicator (letters get chucked up).
'a'+'teach'+'in'='ateachin'
'ateachin' with letters rearranged gives 'CHINA TEA'.

Can you help me to learn more?

(Other definitions for china tea that I've seen before include "cuppa?" , "Eastern drink" , "Leaves for drink" .)

I've seen this clue in the Evening Standard.

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