The difficulty we have is that while the OP has been consistent in their story (see post #37), it's a fundamentally unlikely one. While it's not for me to put words into their mouth, I think that the OP may recognise the problem of lack of plausibility - hence their willingness to consider paying a settlement while asserting their innocence. But it's one thing to (however unwillingly) pay a settlement while proclaiming your innocence, and another to be taken to court and be publicly accused of wrongdoing - which could explain their determination to defend themselves there.
Like many other contributors here, I think the best available advice is to try and settle this matter before court. I appreciate that the OP does not have the amount now claimed by TIL to hand for a settlement: that being the case it might be worth seeing if a courteously worded letter or email enquiring if it would be possible to bring the matter to an end for the original proposed settlement amount (something like £87 if I remember rightly) would work. This would be on the basis that TIL are probably as sick of the sight of this matter as I expect the OP to be.
If that won't work, then the OP's only option will be to go to court. I'm not sure if we've mentioned that this allows one last opportunity to settle matters out of court in that we hear from time to time of people finding the prosecutor before everyone physically goes into court, and agreeing a settlement there and then. But in preparation for that not to work, the OP needs to
- be absolutely clear what the charge is
- be prepared to establish the facts through the evidence they hold and witnesses they can call. At this point they need to remember that TIL will (a) have their own evidence which may point in a different direction and (b) be entitled to cross examine any witnesses the OP puts up
- once the facts have been established, be prepared to argue that these facts support the OP's position (presumably that they are not guilty of the charge)
There can be no guarantee that the OP will win. But on the assumption that what they have told us is true, I do not see that it is guaranteed that they will lose.