Appealing parking ticket

[Niall]

If it's not taxed or insured and not on the public road its perfectly legal so nothing the DVLA can do about it tbh...

yes there is, they can still contact the registered keeper and threaten with prosocution as if its not taxed it has to be decalered SORN

This.
No matter what, the council are going to charge you and laugh at an appeal as really, your still in the wrong for parking in a space you don't have a permit for however i would be paying it then charging it to your landlord because he hasn't sorted his shit out (just deduct it from the next rent bill!)
As for the corsa, phone DVLA and explain it has been dumped and put in a request for the log book. Soon as you have that (will take weeks mind!), scrap it your self.