Blemish of British group (4)
I believe the answer is:
blot
'blemish' is the definition.
(blot is a kind of blemish)
'british group' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'group' becomes 'lot' (lot is a kind of group**).
'b'+'lot'='BLOT'
'of' is the link.
(Other definitions for blot that I've seen before include "Dark mark/stain" , "stain on reputation" , "Spot of ink, paint etc" , "Blemish made with ink" , "Smudge of ink" .)