It's based on the fact that poor people would tend to live in subsidised housing in the UK known as a council estate. Council estates have improved a great deal in the past 10-20 years but some are still suffering from anti-social behavour brought about by Chav and Urban wannabee behaviour by kids and young adults who are simply bored and lacking identity or a sense of community.
Steve: Mr T could pull it off but she's just council.
Eg. Council toothpaste = Water
Council pop = Water
Council boyfriend = One night stand
Council flat = a council flat
Dave: I got a council taxi.
Eve: No shit! You mean you walked over 5 miles home???
Michael- yea man council meeting tonight.
Anthony- ill have to pick up then.