Small entrance at the back, invoicing market (12)

I believe the answer is:

billingsgate

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'market' is the definition.
(London market)

'small entrance at the back' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'entrance' becomes 'gate' (type of entrance).
'at' means one lot of letters go next to another (I've seen this in other clues).
'the back' becomes 'billing' (I am not sure about this - if you are sure you should believe this answer much more).
's'+'gate'='sgate'
'sgate' after 'billing' is 'BILLINGSGATE'.

'invoicing' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for billingsgate that I've seen before include "Swearing" , "London fish market" .)

I've seen this clue in The Daily Express.

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