From the summons you have posted, the court has gone straight to listing a full trial, without a separate pre‑trial review or case‑management hearing in between. This is unfortunate, but it seems to be happening more and more as the goal is to resolve matters in courts with fewer hearings.
That means you should now treat 10 June as a real trial date, not as a first appearance or an administrative review. GTR will be preparing on the basis that this is the trial: they will have to consider which witnesses to call, review the inspector’s statement, check the file and be ready to present the case. In other words, from the court’s point of view, the case has moved into the trial phase.
Once a case is listed for trial and the prosecutor has done work to get it ready, they are entitled to ask the court for higher prosecution costs to reflect that preparation, rather than the much lower figure that would apply on an early guilty plea. For guidance for magistrates’ courts costs are around £85 for an early guilty plea, around £400 for a late guilty plea on the day of trial, and around £650 for a full trial if you are found guilty. This should give you an idea of how costs escalate as a case approaches or reaches trial. GTR are not the CPS, but they will usually pitch their cost request in a way that reflects whether they have had to prepare for and attend a trial.
You therefore have a genuine cost–benefit decision to make now. One option is to keep your not‑guilty plea and run up to the trial date, continuing to chase GTR for an out‑of‑court settlement. That keeps alive the possibility that they may still agree to withdraw the prosecution, even very late in the day, and it also leaves open the chance of a “court‑door” settlement if you speak to the prosecutor on the morning of the hearing. The downside is that if no settlement materialises and you change your plea to guilty on the day, you will be doing so at a point where GTR can legitimately say they have done the work for a contested hearing and ask for trial‑level or late‑plea costs, not the cheaper early‑plea figure.
A second option is to accept that GTR may not settle and change your plea to guilty before the trial, so the court can sentence without a contested hearing. That means accepting a conviction and its implications, but it allows the court to treat this as a case resolved without trial, with correspondingly lower prosecution costs. As we've already said, sentencing guidelines also link the level of credit for a guilty plea to how early it is indicated, so changing course in advance rather than at the door of the courtroom is generally better both for the fine and for costs.
A third option is to instruct a solicitor with experience of railway prosecutions. A solicitor cannot guarantee a settlement, but they may be more effective at getting someone at GTR to look at your file properly and respond to your existing offers, and they can also manage the court process so that, if a settlement is not possible, any guilty plea is entered and dealt with in a way that minimises the financial damage. You would, of course, have to pay their fees, but the idea is that this buys you a better chance of avoiding trial altogether and, even if not, keeps control over the timing of any plea and the level of costs you face.
In short, the court has moved you into a trial listing on 10 June, and GTR will be preparing on that basis. From here, the key decision is how much additional cost and risk you are willing to carry in the hope of a late settlement, and at what point you would prefer to cut your losses by changing your plea rather than allowing the matter to become a fully contested trial.