Stock answer about new and current Bullingdon Club members, say (8)
'bullingdon club members say' is the definition.
(Bullingdon Club is an Oxford university club)
'stock answer about new' is the wordplay.
'stock' becomes 'oxo' (stock for cooking can be made from Oxo cubes).
'answer' becomes 'ans' (A common abbreviation).
'about' says to put letters next to each other.
'new' becomes 'ni' (I can't explain this - if you can you should give a lot more credence to this answer).
'ans' after 'ni' is 'nians'.
'and current' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for oxonians that I've seen before include "college types?", "Members of Oxford University".)