Opponent of BBC, some might say? (4)
I believe the answer is:
anti
'opponent of' is the definition.
(someone who is anti- something)
'bbc some might say?' is the wordplay.
'bbc' becomes 'auntie' (nickname for the BBC).
'some might say?' indicates a 'sounds like' (homophone) clue.
'auntie' sounds like 'ANTI'.
(Other definitions for anti that I've seen before include "Definitely not pro" , "one opposing?" , "on the other side" , "Negative vote" , "not favoured" .)