//....that's unlikely to happen because a fine under these regulations cannot be appealed, the only recourse is to refuse to pay, and likely end up with a criminal record and an even bigger fine (so few would dare).//
We need to take care with the terminology, mush. Only a court can impose a fine (for any offence). "Authorised Persons" can offer fixed penalties which the accused can accept to discharge the offence without court action. If he disagrees with the basis on which the fixed penalty is offered he can decline to pay. Then he will be prosecuted and if he pleads Not Guilty the burden falls to the prosecution to prove the offence to the criminal standard ("beyond reasonable doubt"). Only if he is convicted can a fine be imposed.
This is no different to any other offence where a Fixed Penalty may be offered (for example, speeding). The driver has no obligation to accept the fixed penalty. He cannot "appeal" it as such - he either accepts it or doesn't. But he can decline the offer (or simply ignore it) and see the matter dealt with by a court.