Matter that is dividing households in region round London (4,8)
I believe the answer is:
home counties
'region round london' is the definition.
'matter that is dividing households' is the wordplay.
'matter' becomes 'count'.
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'dividing' is an insertion indicator.
'households' becomes 'homes'.
'count'+'ie'='countie'
'countie' inserted into 'homes' is 'HOME COUNTIES'.
'in' is the link.
(Other definitions for home counties that I've seen before include "Come in" , "Area surrounding London" , "land around London" , "Region of SE England" .)