Dimwit ran into stores at Oxford, beginning to panic (6)
I believe the answer is:
muppet
'dimwit' is the definition.
(I know that dimwit can be written as muppet)
'ran into stores at oxford beginning to panic' is the wordplay.
'ran into' becomes 'met' (run into can mean to meet or encounter).
'stores' indicates putting letters inside.
'at oxford' becomes 'up' (term meaning at university).
'beginning to' indicates taking the first letters.
The initial letter of 'panic' is 'p'.
'up'+'p'='upp'
'met' enclosing 'upp' is 'MUPPET'.
(Other definitions for muppet that I've seen before include "Kermit, Fozzie Bear or Animal?" , "Fool - Jim Henson creation" , "Idiot" , "Weak person (informal)" , "Kermit or Miss Piggy, say" .)