One swims British river from South West, maybe (5)
I believe the answer is:
bream
'one swims' is the definition.
(bream is a kind of fish)
'british river from south west maybe' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'river' becomes 'r' (abbreviation).
'from south' says the letters should be written backwards.
'west maybe' becomes 'Mae' (actress Mae West).
'mae' backwards is 'eam'.
'b'+'r'+'eam'='BREAM'
(Other definitions for bream that I've seen before include "Carp relative" , "Fish - British classical guitarist, b. 1933" , "Amber (anag) - fish" , "Fish found in amber" , "Fish - English guitarist" .)