As I understand things, when a train company cites criminal law, its compensation - whether in court or out-of-court - is limited to that which puts it back into the position it would have been in had the alleged offence not been committed. The fare component of that is taken as the additional amount that the passenger would have paid, evidenced for example by past behaviour (e.g. buys weekly seasons) or else by what a typical passenger like them does. There are only two ways to give the passenger a penalty: Either impose a Penalty Fare or secure a conviction and let the court impose a fine. There is a bit of scope for the train company to get away with being slightly imaginative in what it asks for when the stakes are low but it's a fine line and we see shades of some of what the Post Office was doing in some of the letters shown on the forum. Personally I consider most of the administration charges we read about on here to be unjustifiably high, as if they are attempting to obtain contributions to overheads that would have existed irrespective of the individual passenger's behaviour. The agreements the train companies operate within provide no scope for creating any unofficial system of penalties outside the law or for requesting payments beyond what is needed to properly compensate them on the basis described.
However, separately, the contract already specifies the fare that is due in given circumstances. This could lead to a higher amount being due than the train company would receive as compensation for an alleged criminal offence. Using civil law, for example, might sometimes indeed lead to higher fares based on Anytime Singles one journey at a time needing to be paid, with no credit allowed for invalid tickets and no possibility of calculations based on season ticket rates.
After a conviction, if the train company believes the contract specified that a higher fare was due than it received in compensation, then nothing stops it from inviting a civil court to agree and order additional sums to be paid. (It's out-of-scope for the criminal court to consider whether anything extra is due contractually. The current wording of the contract might make this harder than it ought to have been - circumstances vary. Nothing prevents the contract from specifying payments that amount to penalties.)