I generally advocate that here on the forum, we focus on informing the people who come to us for help and leave out the moral judgement. However in this case I find it necessary to say in no uncertain terms to the OP: you have cost your daughter 400 quid and a lot of stress. Not the railway, you.
Your daughter travelled on an invalid ticket; she intended to do so. As the document states this is an offence under section 5.3(a) of the Regulations of Railways Act 1889. This is a criminal offence, in the same way that stealing a bar of chocolate from Tesco’s is also a criminal offence. The railway was, and is, fully entitled to charge your daughter in the magistrates and give her a criminal record for a year. Instead, Chiltern, one of the harshest train companies with regards to prosecution, decided to charge a settlement cost of 60 quid, having known of the possibility of further invalid travel. I cannot overemphasise how lenient this offer is. Chiltern usually charge people 150+ quid on administration alone, and you have gotten away with a penalty fare amount on an offence which technically cannot be penalty fared. Given you later found 300+ quid for a lawyer, I cannot imagine that it was immensely difficult to pay said 60 quid on the spot. Instead you choose to ignore the offer, because it was… “just a matter of 3 quid”? That’s not how the law works. Hundreds of other people on this forum in much more difficult economic situations would have given a lot to receive this kind of offer, not to mention people charged by TfL.
Having been placed in this immensely lucky position and having decided to scorn it, Chiltern was apparently in a good enough mood to give you a *second* settlement offer, which is nearly unheard of even from pragmatic companies like GTR (Thameslink). You decided not to act on it until it was too late, then act surprised when the offer further escalated. You then asked to pay the previous offer, as if entitled to it. Your daughter is guilty of a criminal offence. That the actual loss is 3 quid does not legally matter. Chiltern have taken every possible reasonable step to entice you to co-operate, far beyond what most would call reasonable measures, and in a manner which many could call unfair compared to the way they crack down on other fare evaders. You have refused their reasonable and friendly offers. What did you expect to happen? “Oh, this person thinks our offer is too expensive, I suppose we’ll just drop it then”?
I do not make any comment on whether it was an honest mistake. But even if it was, honest mistakes can cost money. If I trip in a supermarket and knock down a vase, I probably will need to pay the cost of the vase plus quite a bit more for the cleanup costs. It would be a very foolhardy person to argue “it was a crack on your floor, not my fault, I shan’t pay it”.
If a significant portion of people responded to settlement offers in the manner you have, I cannot help but understand why railway companies are so strict on their offers for most cases of avoided fares. I only hope that your daughter has learnt some life lessons from this incident that you apparently haven’t.