I now await a post from the usual suspect stating that this is bad advice but offering no explanation as to why it is bad advice and then ignoring any request to provide explanation.
In fairness to the poster in question, whom I believe to be a very long-serving, well-respected and highly qualified member of this form, any advice may turn out to be poor advice with the benefit of hindsight, which none of us have. If the OP pays, when the TOC would not in fact have prosecuted (after all, he/ she had a valid ticket, so it might be argued that the chance of being prosecuted is substantially lower than with a 'normal' unpaid PF), then advice to pay would, with hindsight, have been bad advice. Conversely, if the OP does not pay, and ultimately ends up being convicted, then advice not to pay would, with hindsight, have been very bad advice indeed.
I do not think it is helpful for forum members to tell each other that they are giving poor advice, unless the advice is blatantly incorrect, profoundly unwise or likely to lead to the commission of criminal offences, in which case a brief explanation should be given (and the moderating team may well intervene anyway).
I cannot claim to be completely innocent on this front, but, nonetheless, I admit that it frustrates me that certain member(s) will appear to advise as follows:
1) Passenger makes mistake as to ticket validity: Passenger must pay whatever is demanded, and TOCs are entitled to charge £80+ for spending a few minutes issuing the PF/ UFN/ demand for payment in lieu of prosecution (which might fairly be characterised as a form of ransom demand, particularly when the traveller has neither admitted liability nor requested any form of settlement).
2) TOC makes mistake as to ticket validity: Passenger must pay whatever is demanded anyway regardless or be convicted despite their complete innocence; any attempt to recover any amount at all is doomed to failure, and the passenger is not entitled to charge for their time spent dealing with the matter.
Pragmatism is one thing, but simply paying unenforceable ransom demands left, right and centre does not strike me as being particularly pragmatic, and urging others to pay such demands seems to me to be a counsel of despair.
However, this is of limited relevance to the OP in his/ her specific case, who must make a decision for himself or herself based on a number of factors, some of which we may not even be aware of.
My only specific advice at this point is:
1) to appeal promptly, if he/ she hasn't already done so, and;
2) to delay a decision until towards the end of the 21 day period giving for paying the invalid PF.
If the OP chooses to pay at this point, he/ she will not have lost anything compared to paying now, and there is a chance that the appeal might be upheld in the meantime. However, if the OP has not paid the invalid PF within the 21 day period given for payment, the stakes will rise in that the amount demanded to be certain of avoiding prosecution will be inflated by supposed 'administration fees'.
If the inflated amount demanded is not then paid, there is a chance that nothing more will happen, but there is also a chance that the invalid PF and its associated 'administration fees' may be cancelled and the OP prosecuted.
One may well infer from my previous post what I would do if in the OP's position, but perhaps it is easy for me to be a 'keyboard warrior' when I am not the one who would have to deal with the consequences if it all goes wrong.