I just thought I would share my experience at court for anyone that has also been summoned at Lavender Hill by TfL.
You may see in the above threads that I was summoned by TfL after being caught with a 60+ photo card.
So basically you walk in, get searcher, and are then just in a waiting room with all the other offenders, all TfL cases. There is the 10am session and the 2pm session, with three courts. Make yourself known to the clerks or you will be waiting a lot longer (like I was lol). One of them will then take you into a room, explain what will happen, as you to sign for any other journeys that you are suspected of, and then you go back to the waiting room. I just signed the ones that I did do because it was the same journey that I was caught on, but really and truly you can just say that you are only guilty of what you were caught for. They would have to prove the other journeys which, quite frankly, they do not have time for (I spoke to a legal adviser who was buddy buddy with the chief TfL prosector) - but the choice is yours.
Eventually they will call your name, and you will be in front of the court. Three judges straight ahead, someone on a computer also in front of you will just ask you to confirm name and address. And to your left will be two people, one of them the prosecutor for TfL. They will read out the charge and ask for your plea. From what I remember, the prosecutor will try and make it seem worse than it is, and search for the £375 in costs etc (which is such bs but what you going to do). The judge will then ask you if you got anything to say, then ask you to sit for a few moments before their verdict. They will read out what you have to pay (£375 in costs, victims surcharge, etc). I ended up with a £551 fine. I will pay this in £50 instalments over 12 months.
And then you're done. Roughly 5 mins, that is it. It looks scary, but you know what will happen now, and literally everyone in the waiting room is going through the same thing. It is so much more common than you think. Sure it is a criminal record, but as my advisor said, it is not theft or fraud or anything serious - you avoided a train fare, employers are not going to hold that against you. Your life will not end, over 20,000 are in the same situation annually.
Thank you to those in the forum for your help, even if a few of you clearly get a kick from people being in some sort of trouble (you know who you are). I hope this helps the relevant people.