British League's problem affecting one member (6)
I believe the answer is:
bunion
'problem affecting one member' is the definition.
(swelling on a foot)
'british league's' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'league' becomes 'union' (I've seen this before).
'b'+'union'='BUNION'
(Other definitions for bunion that I've seen before include "Painful swelling at base of big toe" , "Swelling on the foot" , "Painful swelling of the big toe joint" , "Foot fault" , "Swelling at base of toe with thickened skin" .)