I will definitely address the fact that I do not accept nor deny fault as no offence has been referenced in the letter. But maybe it might aggravate the court if I don’t just directly cooperate. But it makes more logical sense to actually ask what it is they are accusing me of, before I start offering information.
I'll preface this by saying I am not a solicitor and this isn't legal advice.
Courts do not get "aggravated". You are entitled to refuse to answer questions. A magistrate may draw an inference from that refusal but it will not "aggravate" them. It is, in some circumstances, wise not to answer questions under caution when you do not have a legal representative present and that is a perfectly adequate justification for you using that right.
A solicitor would lay out the pros and cons in a proper way - I am not a solicitor - but I think you should be reminded again of your right to simply not answer a terrible, open question
which has been set as a huge trap to gather evidence against you.
You are, unquestionably, guilty of the strict liability Bylaw offence of failing to present a valid ticket. Tapping through the barrier on someone else's card and being stopped on the "paid" side by revenue officers waiting for someone to do it means you were caught. No intent is required to be proven, a bit like speeding.
A Bylaw conviction is not recordable - so it doesn't get entered on the Police National Computer and you won't have a "criminal record" - at least by that definition anyway. A Bylaw offence is strict liability and very, very minor in the scheme of things.
A more serious offence is the Regulation of Railways Act (RoRA) 1889, which requires you to have the intent to "avoid payment" of the fare. Tapping someone else's Freedom Pass and having a poor excuse as to why you did that - especially if other instances of misuse come to light - may invite a court to believe you did intend to avoid payment and convict you of this offence, but you must be charged with it by TfL.
However, we see most often that TfL dispose of offences even where clear intent is shown, by way of Bylaw prosecutions instead. This is a much simpler offence to prove and much easier to arrange a case for. TfL prosecute God knows how many people each year so this is something of an efficient machine and they don't like the faff of RoRA prosecutions.
Isn’t that me just setting myself up to attend a court hearing?
TfL do not settle, by habit. There will almost certainly be a court hearing but you do not have to attend in person and can submit your mitigation in writing. Your objective now is to ensure your offence is only a Bylaw one and not to give them any cause to prosecute you for offences involving intent. Hence,
if it were me, I would not answer the questions in the letter. During your stop you probably inadvertently gave them small pieces of evidence like a motive (I'm a student, I don't have a lot of money, I'm borrowing this coat) which may be used against you if you pleased not quilty and were cross-examined.
My rule is to let them take their time to uncover the evidence, especially if you have used the Freedom Pass before. Do not do it for them.
In any case, whatever you choose to do with your reply, do post a draft on here and posters will be able to advise on tone, clarity and make suggestions.