Cheap digs found in county one time (6)
I believe the answer is:
bedsit
'cheap digs' is the definition.
(I've seen this before)
'county one time' is the wordplay.
'county' becomes 'beds' (abbreviation for Bedfordshire).
'one' becomes 'i' (Roman numeral).
'time' becomes 't' (abbreviation).
'beds'+'i'+'t'='BEDSIT'
'found in' is the link.
(Other definitions for bedsit that I've seen before include "One-room home" , "little accommodation" , "One-room accommodation" , "Small residence" , "Single room for living" .)