You are in a very weak position here I'm afraid to say.
You need to try to communicate clearly with Southeastern that you are happy to pay them compensation in respect of the instance of using a child ticket to which you weren't entitled where you were caught. Then make an offer that's the most you can afford and emphasise you have no other access to funds and no income at present, while offering to make further payments later.
Southeastern may accept a small payment from you now and give you a decent time to continue paying later. If they refuse this, they will prosecute you for one instance of travelling without a valid train ticket, most likely. You can plead guilty to this at the first and ensure that you highlight in so doing that you're unemployed and have an income of near zero at present. There's a specific form you should send to the court that declares some financial information about you. The court will most likely order you to pay some costs and compensation to Southeastern and importantly will discount your fine and base it on your low income. You would usually be offered a discount on the fine as a result of pleading guilty. You would likely qualify to pay the amount the court orders over time, although if you take this option it is vital you keep up with the repayments.
If the court orders you to pay a fine and surcharge these do not go to Southeastern, only the costs and compensation amounts. Therefore Southeastern have a small incentive to offer you a payment plan because they receive all of this money if you keep up with repayments.
