My opinion on the question of having been given permission to travel without a ticket is simply this:
If that is true, and wholly true, in respect of your entire ticketless journey, and if that is going to be an adequately persuasive reason for avoiding prosecution for ticketless travel, then - you really don't want to be having that argument in a Court, where the prospects of failure are stressful, expensive and long-lasting, and the odds are not encouraging.
That is a simple discussion which a local solicitor who specialises in Criminal Defence work can have with the Company's Prosecutions Manager over the phone. It is quick, very likely to succeed, and is only going to cost you £100 or so.
If the permission to travel given three months ago, which no one dealing with a few million passengers a year is going to remember now, and you didn't get any statements from them at the time, is not available as Evidence, then you shouldn't be relying on it, and certainly shouldn't be expecting a Court to find in your favour. (please disregard suggestions that evidence that is unavailable is Evidence, it isn't, or that answers from people who have not been interviewed is Evidence, it isn't). Where the Evidence doesn't exist, then you shouldn't be considering it as helpful, regardless of what actually happened on the journey in question.
If you take the DIY approach, which some have suggested, of saying 'Not Guilty - I was permitted to travel but I have no evidence' and the Company has whatever evidence it has (you haven't told us, despite my asking twice, so I'm assuming that you don't know), then you are faced not with the odds of succeeding, but with the odds of expense.
I'll guess your odds of success before getting to Court are 80%, with professional assistance.
Your odds of succeeding in Court with a Not Guilty claim are 70% with professional representation and 10% if you adopt the DIY approach.
The odds of expense are, if you succeed : no fine, no costs, but a lot of your time and anxiety.
If you fail, the fine, plus costs, plus Victim Surcharge plus Criminal Conviction Charge will be £1000 to £1500, and a lot of your time and anxiety.
Arguing the same point where it really matters should only be done with well prepared research and evidence, and will come at a high price. I can't advise you to do that.
There is a legitimate concern about the scope of Railway Byelaw 18 (3) iii or 25 (1) i. But it is not appropriate for you (as someone who's counsel comes from an internet forum) to be challenging that at your risk. That is for someone whose costs are properly underwritten by others to argue.