Sew at Posh's poorly designed and grim clothes factory? (9)

I believe the answer is:

sweatshop

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'factory?' is the definition.
(I know that sweatshop is a type of factory)

'sew at posh's poorly' is the wordplay.
'poorly' indicates anagramming the letters (a poor spelling).
'sew'+'at'+'posh'='sewatposh'
'sewatposh' with letters rearranged gives 'SWEATSHOP'.

'designed and grim clothes' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for sweatshop that I've seen before include "Place employing exploited workers" , "cheap workplace" , "Factory with low pay and long working hours" , "Factory (derog.)" , "Exploitative factory" .)

I've seen this clue in the Sydney Morning Herald.

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