Is it not the same as 'failing to display a tax disc' (or whatever)? That is, it doesn't matter if you're taxed or not - it's the failing to display bit that's the offence.
Sounds perfectly reasonable to me, otherwise what's stopping you putting an old ticket face-down on the floor/seat/dash of your car... if the warden comes up and books you... you wait around for someone to return to their car... get/buy their ticket off them... and send it off claiming you had a valid ticket but it had just dropped off. Sure, wouldn't work for reg-encoded tickets but many aren't like that.
If it was for parking on the public highway then you can appeal to an independent adjudicator. They must inform you of this at some point in the procedings: this is not the same as appealing to them (Vinci/council who enforce parking restrictions) so hold out and do the independent appeal. You can do so in writing or represent yourself in person. The adjudicator will be something like a low-ranking solicitor and the hearing fairly informal. If you lose you'll have to pay the penalty: you'll miss the early-payment discount (which you say you have already) but won't have to pay any more than that.
If it was parking on private land then AIUI if the owners of the land have made it clear (e.g. by prominently-displayed signs) that if you park there you're liable to be charged for it or even clamped, then a contract exists between them and people parking there which allows them to sue you for the agreed amount (as indicated on the signs). The signs have to be obvious: it's no good to you if you choose not to read them. Look up Wade v. some London Borough (Shoreditch? Hackney?) in BAILII.
There may be other situations where it's not public highway but there are bye-laws which apply. Dunno about those.
IANAL, but FWIW I went through the public highway appeal course with ourlocal council (and lost) and the private land business with Observances Parking Services and won (basically ignored them and they went away :-)
Because the notice to owner has allegedly been sent and ignored for a certain period, it appears you lose the right to appeal. By the time the charge certificate arrives, it's pay within 14 days or it goes to court. However, even at this stage, you can apparently complete a statutory declaration form where you swear to the court under oath that the NTO was not received. The original ticket may then be re-issued by the council, and the normal appeal process can begin. If I get back to that point, I shall be happy because the Vinci scam only works by leap-frogging the appeal process, and they don't have to do anything other than forget to send the NTO. This means all those tickets that are issued and can't be stuck on the windscreen and photographed may still be a source of revenue for them.
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