In terms of which one applies to you, if you bought a child's ticket without the correct railcard it would be the first offence of Travel on a railway without paying the correct fare contrary to section 5(3)(a) of the regulation of railways act. In any case as far as your concerned you should address the fact you paid for the incorrect fare. I'd leave out any reference to legislation as its up to the train company in regards to what they charge you with based on the available evidence and public interest (railway byelaws vs reg railways) and by referencing a specific offence say regulation of railways I would've thought your just encouraging them to charge you with the more serious charge . I'm sure others will have more in depth advice on how to reply, but as someone else mentioned your essentially asking for an out of court settlement.
The letter needs to be not too wordy (they deal with a lot of cases) nor too little that implies you don't care. the letter needs to come from you but you can post it here before you send with redacted details for others to look at and advise.
Hi! i have a draft of my letter here;
Thank you for your email regarding the incident on 29/01/2025.
I would like to begin by sincerely apologising for my actions. I understand that purchasing a child’s ticket and giving a false date of birth to the inspector was completely wrong, and I deeply regret my behaviour.
At the time, I was under significant personal and financial pressure. I am a full-time student and had recently lost my part-time job, leaving me struggling to afford even basic essentials like food. In a moment of panic and desperation, I made a poor decision to lie about my age in order to travel using a child’s ticket. I know now that this was dishonest and unacceptable, and I take full responsibility.
I never intended to cause harm or avoid paying my fair share — I made a foolish choice that I now deeply regret. I understand the seriousness of this situation and want to make it right.
I would be extremely grateful if you could consider resolving this matter without proceeding to court. I am willing to pay any outstanding fares and associated costs, and I can assure you that nothing like this will ever happen again.
Thank you very much for taking the time to read this and for giving me the opportunity to explain my situation.
Yours sincerely,