Limits of council house register affected county (15)
I believe the answer is:
gloucestershire
'county' is the definition.
(I know that Gloucestershire is a county)
'limits of council house register affected' is the wordplay.
'limits of' suggests removing the centre.
'affected' is an anagram indicator.
'council' with its middle removed is 'cl'.
'cl'+'house'+'register'='clhouseregister'
'clhouseregister' with letters rearranged gives 'GLOUCESTERSHIRE'.
(Other definitions for gloucestershire that I've seen before include "English county" , "Potter's tailor had it round" , "area around Cheltenham" .)