I would note that a number of experts here have asked you questions about this incident, and you have chosen not to give this information. Which in turn means that you are not able to benefit from this expertise if you hold things back.i have a letter of proof to state my mental well being, it was from the doctor for me to provide my university options to prove my extenuating circumstances. It is a little brief and I told my DR what areas need to be covered.
But from what you've said so far, the letter from the doctor is potentially useful mitigation, but it's not really extenuating, which means "making something forgivable". There is an argument - implied just above by SteveM70 - that if you knew about these issues then you should thereby be informed as to how to avoid problems. So if you steal something from a shop, the fact you are have mental health issues does not make it forgivable, but it provides a context in terms of deciding what should happen to you - but it could be argued that if you know you have problems you would try extra hard to avoid getting into difficulties with the authorities. I've listed your health conditions as a mitigation earlier, along with a number of other factors, and I missed an important one, namely that you have very limited income, from what you've said. From what we know, card mis-use is an area where TfL will take you to court - I don't think that's the right thing to do but my views are meaningless, this is just how TfL works. So your mind-set needs to be in realistic damage limitation, not avoiding responsibility or hoping it can be argued away.
But at the same time I don't think this is quite as awful as you understandably think it is right now. All this shall pass.