Goes off Mon-Fri around city area (6)
I believe the answer is:
decays
'goes off' is the definition.
(I've seen this before)
'mon-fri around city area' is the wordplay.
'mon fri' becomes 'days' (I can't explain this - if you can you should believe this answer much more).
'around' is an insertion indicator.
'city area' becomes 'EC' (EC is a London postcode area).
'days' going around 'ec' is 'DECAYS'.
Can you help me to learn more?
(Other definitions for decays that I've seen before include "Decomposes or falls into ruin" , "Goes off" , "Rots and decomposes" , "Rots, disintegrates" , "Rots, moulders away" .)