Shabby state of children in over half of Essex (9)

I believe the answer is:

seediness

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'half of essex' is the definition.
The definition suggests a singular noun which matches the answer.

'shabby state of children in over' is the wordplay.
'shabby state of' becomes 'ess' (I can't explain this - if you can you should believe this answer much more).
'children' becomes 'seed' (I've seen this before).
'over' says to put letters next to each other.
'seed'+'in'='seedin'
'ess' put after 'seedin' is 'SEEDINESS'.

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(Other definitions for seediness that I've seen before include "Sordid or squalid quality" , "Sordidness, grubbiness" .)

I've seen this clue in The Telegraph.

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