Dairy product not British, say (5)
I believe the answer is:
utter
'say' is the definition.
(to utter something is to say or speak it)
'dairy product not british' is the wordplay.
'dairy product' becomes 'butter' (butter is a kind of dairy product).
'not' indicates named letters should be taken away.
'british' becomes 'b' (abbreviation e.g. in BBC).
'butter' with 'b' removed is 'UTTER'.
(Other definitions for utter that I've seen before include "Speak, articulate" , "Express audibly" , "Sheer" , "Articulate, express" , "Total < state" .)