Questioned under caution? What do you mean? I am over 18 yes...I admitted that I had not swiped my card at the station. I am panicking really badly. I fear I am going to be sent to court and / or jail.
Try not to panic.
What I meant by questioned under caution is, did the RPI state the following, or words to it's effect (You'd know if you were cautioned);
"You do not have to say anything, but it may harm your defence if you do not mention, when questioned, something you later rely on in court. Anything you do say may be given in evidence"
It's the same as when questioned by Police, or when arrested. In your case you won't have been arrested obviously, and this would have been made clear. When questioned under caution the RPI would have written down everything he asked you, and what you replied. This is admissible as evidence in court. That's not to say if he didn't caution you he can't use his notes as evidence, it just makes for much better evidence under the Police And Criminal Evidence Act (PACE).
Prison is only a possibility on subsequent offences of fare evasion (You'd only need to realistically worry if you were extremely persistent, and even then Judges/Magistrates are reluctant to pass custodial sentences as prisons are already very crowded places!).
You should reply to this letter saying you are extremely sorry and this was out of character. I advise you tell them that this was the first time you've done anything like this and will never do anything of the sort again. I'd also tell them that any conviction could affect your current of future employment. At this stage it would be wise to ask the TOC if they'd be willing to settle the matter by you covering all reasonable administration costs incurred by them (Not sure which one it is, but most are willing to settle administratively for a first offence as long as no abuse towards staff was present or there were more than one offence at the same time). You're usually looking at around the £100 mark. I wouldn't delve in to your depression and anxiety, as you don't want to be seen to be making excuses for your actions.
They don't have to accept your offer, but you'd be frankly silly not to try. You can offer to settle the matter right up to and including the court date if it got that far, but obviously the costs would be higher as the train company would have used more resources the further down the line it gets.