Whilst undoubtedly the simplest, least stressful and least risky approach is to accept the settlement and pay it, I'm actually somewhat in doubt of whether the TOC has a case.
They cannot impose a Penalty Fare as that was not originally done from what we have been told, and Penalty Fares cannot be given after the traveller has left the railway (well, perhaps whilst they are attempting to leave, but certainly not days or weeks afterwards).
I don't see that they have any grounds to pursue a RoRA prosecution, as they have no evidence that the fare has not been paid or that any fare has been avoided (or attempted to be avoided). The fact that no photocard was used in conjunction with the ticket is really an irrelavnce - S5(3)(a) of RoRA is about whether or not the fare has previously been paid. This is not about OP having a child-rate ticket, or a Railcard discounted ticket when they held no Railcard. They held a season ticket which was itself valid (in date, correct route etc.) - they merely did not have a photocard. I think the TOC would find this a risky case to try and take to Court, seeing as there is no evidence of any financial loss (or fare not paid).
Byelaw 18 would therefore usually offer the 'back-stop' in a situation like this where the passenger has paid their fare but the ticket is still considered invalid. It is a fairly unusual "grey" zone, to be honest. The thing is - Byelaw 18 is unlawful in my view. It is secondary legislation that attempts to modify primary legislation, and that is not permitted, except where specifically authorised by the delegating primary legislation. There is no Act that I am aware of that permits Byelaw 18 to effectively change RoRA such as to remove the requirement to prove intent, and hence Byelaw 18 cannot be valid in the absence of such an Act.
Would a challenge on the above lines be easy? By no means. In fact it may well cost significantly more than simply paying the settlement offered now (if you are still found guilty and don't wish to appeal, for example) and it would almost certainly involve a lot of stress - but there is a distinct possibility that, if you pursue it correctly, you would end up no worse than you are now, and that you could avoid paying the settlement. There may well be enterprising solicitors who would be happy to take on a case here, either pro bono or on the basis of recovering their costs from the TOC if and when the case is won.
If you're hesitant around paying the settlement I would contact a few criminal defence solicitors and see if you can arrange a free consultation with them. I would imagine most high-street solicitors would not really be interested by something like this which is itself unusual (railway prosecutions are less common than motoring prosecutions for example), and perhaps a risk for them (if the Magistrate who deals with the matter doesn't fully understand the points being made, and therefore finds OP guilty).
Ultimately, it is up to the OP as to whether they wish to take the "easy" route by paying the settlement offered (but which they know will cost them £140 odd which there is a good argument to say they should not be paying), or whether they want to end the 'tyranny' of Byelaw 18 by challenging its mere existence, a riskier and more stressful approach, but one that could see them get "one over" the TOCs and, more importantly, hopefully not out of pocket.
