How about
Dear Prosecutions Manager,
I'm writing to apologize for traveling without a valid ticket from [home station] to London Bridge on 31 October 2024. I realize this was a serious oversight on my part, and I’m truly sorry for any inconvenience caused to Southeastern Railway.
This experience has made me more aware of how important it is to follow fare policies to keep things fair for all passengers. I take full responsibility for my actions, and I’m committed to making sure this doesn’t happen again.
I would be very grateful for the chance to settle this matter without it going to court. I’m more than willing to cover the fare I owe, along with any costs Southeastern has incurred in dealing with this situation. I hope you will consider my request, and thank you for your understanding.
Yours faithfully,
[Your Name]