East Midlands town doctor set child free (12)

I believe the answer is:

chesterfield

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'east midlands town' is the definition.
'chesterfield' can be an answer for 'town' (I've seen this before). I am unsure of the 'east midlands' bit.

'doctor set child free' is the wordplay.
'doctor' is an anagram indicator.
'set'+'child'+'free'='setchildfree'
'setchildfree' with letters rearranged gives 'CHESTERFIELD'.

Can you help me to learn more?

(Other definitions for chesterfield that I've seen before include "Part of Derbyshire" , "Sofa; English town" , "Sofa; overcoat" , "Midlands town" , "somewhere to sit" .)

I've seen this clue in The Guardian.

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