Not having British sausages makes one see red (6)
I believe the answer is:
angers
'one see red' is the definition.
I can't tell whether this definition defines the answer.
'not having british sausages' is the wordplay.
'not having' indicates named letters should be taken away.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'sausages' becomes 'bangers' (banger is a kind of sausage).
'bangers' with 'b' taken out is 'ANGERS'.
'makes' is the link.
Can you help me to learn more?
(Other definitions for angers that I've seen before include "gets hot" , "Maine city" , "Winds up" , "Maddens" , "Infuriates" .)