I’m afraid that the investigators won’t believe you that you were in Central London, you lost your oyster, and didn’t have any money, nor a phone with a payment facility. And you don’t want them to think that you are lying.
So in your reply I would simply apologise for tailgating and promise not to do it again.
Though as noted in the first reply, it’s highly likely that you will be prosecuted, and on the evidence will be found guilty, which will result in a fine and associated expenses of a few hundred pounds.
I see, thank you, I have just finished my response, im not sure exactly what they want, if you have the time I would love a seal of approval haha.
I am writing to you in response to your letter regarding an incident that occured on the ____, where I accompanied my friend through the barrier without a valid ticket. I would like to sincerely and profusely apologise for my actions and take full responsibility. I did not realise the seriousness of my actions at the time, breaching TfL's terms of carriage.
I had been out of the country for almost a year, and my zip card had expired. I entered the tube using my debit card, and at the time, I believed I didn't have enough money to return. However, I know that nothing excuses my actions and I should've found a way around it. Since the incident, I have purchased a new oyster and have been using it correctly, as intended.
I understand that this doesn't recitfy my actions, but I want to emphasise this was a one-time mistake. I deeply regret it, and I hope this does not define me or my future. I clearly understand the importance of my actions and the impact it has on the transport in the city I love. I know I have learnt from this and I will never do it again.
I respectfully request that you consider resolving this matter without further legal action. I would be extremely grateful if you would consider settling this matter out of court by allowing me to cover fees, fines, reimbursments and any administrative costs you deem appropriate to resolve the situation.
Once again, I offer my sincerest apologies and assure you that this won't happen again. Thank you for considering my response.
Yours sincerely,
my name