Labour minister, who once attacked political correctness, claims most of others exaggerated (8)
I believe the answer is:
prescott
'labour minister who once attacked' is the definition.
(John Prescott famously punched a journalist)
'political correctness claims most of others exaggerated' is the wordplay.
'political correctness' becomes 'PC'.
'claims' is an insertion indicator.
'most of' means to remove the last letter.
'others' becomes 'rest' (I've seen this before).
'exaggerated' becomes 'OTT' (short for 'over the top').
'rest' with its final letter taken off is 'res'.
'pc' enclosing 'res' is 'presc'.
'presc'+'ott'='PRESCOTT'
(Another definition for prescott that I've seen is " John --, politician".)