Drink up around British island (4)
I believe the answer is:
elba
'island' is the definition.
(I've seen this before)
'drink up around british' is the wordplay.
'drink' becomes 'ale' (ale is a kind of drink**).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'around' means one lot of letters goes inside another.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'ale' backwards is 'ela'.
'ela' placed around 'b' is 'ELBA'.
(Other definitions for elba that I've seen before include "Exile isle for Napoleon" , "Napoleonic island" , "''Able was I ere I saw . . . .'' (4)" , "Island of Napoleon's exile in 1814-15" , "Napoleonic prison" .)