Any consolidated town and city which (1) was consolidated in 1896, (2) has a mayor and a court of common council, and (3) has a population of more than one hundred thousand, may, by ordinance adopted by the court of common council, authorize the parking authority of such consolidated town and city to (A) enforce the parking regulations of such consolidated city and town, and (B) receive the amount remitted to the town and city for parking regulations under subsection (b) of § 51-56a.