I used to have a friend that bought cars (crappy Fiesta's), fixed them up and sold them on (In some cases swapped engines that had died). He claimed it was a legit business but used to leave them outside his house until they sold, in some cases with no tax!
One day the council clamped about 4 of them and requested he pay fines to release them. I think he also had to tax them so had to get insurance as well even if he had private land to move them to. If not paid, he would have had them removed and disposed of.
I think one of his neighbours might have reported him. I know if I lived next door I would have been pretty P1553d as the parking was horrendous before and it was about 30m from a school!
So yes, if the council deem it to be public land then they might act for you.