Start of Euroscepticism in British right and left as well (7)
I believe the answer is:
besides
'as well' is the definition.
(thesaurus)
'start of euroscepticism in british right and left' is the wordplay.
'start of' indicates taking the first letters.
'in' means one lot of letters goes inside another.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'right and left' becomes 'sides' (I've seen this before).
The initial letter of 'euroscepticism' is 'e'.
'b'+'sides'='bsides'
'e' inserted within 'bsides' is 'BESIDES'.
(Other definitions for besides that I've seen before include "also is available" , "In addition, as well" , "What's more" , "to boot" , "Apart from" .)