Eg, London society — not so English (4)

I believe the answer is:

city

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'eg london' is the definition.
(london is a kind of city)

'society not so english' is the wordplay.
'society' becomes 'soc' (abbreviation in the names of organisations).
'not' is a deletion indicator.
'english' becomes 'ity' (I am not sure about this - if you are sure you should believe this answer much more).
'soc' with 'so' taken out is 'c'.
'c'+'ity'='CITY'

Can you help me to learn more?

(Other definitions for city that I've seen before include "See 5" , "- of God (St Augustine)" , "See 10" , "See 9" , "Charlotte, for instance" .)

I've seen this clue in The Times.

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