First off, Alexandra Palace is a red herring: it just happened to be where the train had stopped, or was nearest to, when the person was caught in First Class without relevant ticket, so never having been to A.P. station is irrelevant.
Secondly, the o.p. doesn't say whether they believe someone may have got hold of their identity in any way, presumably something with the o.p.'s address on it as well. If not, who do they know who knew both their name and address well enough to recite it to a Revenue Inspector, albeit the name may have been slightly corrupted or the R.I. may have noted what was told them incorrectly (unlikely, I'd have thought.)
If I were the o.p. and knew I was innocent I'd certainly demand the prosecution produce the evidence (CCTV, bodycam, and identification documents seen at the time) and, presuming they couldn't given that scenario, ask the magistrate to dismiss the charges. On the other hand, from what can be seen of the redacted letter, it seems some identification was sought and got but the person ('she') declined to answer further questions. Umm, I'm trying to put myself in the magistrate's position, and I'm ex-Probation Service, not that I was ever involved in any fare evasion cases.
Good luck to the o.p. in any case.