Well, we probably expected this would be the next you would hear about the matter.
The letter you have received will give you no indication of the quality of the evidence against you. As some on here have already hinted, it is sometimes seen as an opportunity for the dishonest passenger to incriminate themselves further, or at least to change their story, placing them under even more suspicion!
I can only suggest one course of action, with two variants. That you reply with the absolute truth, which I hope would be compltely consistent with the statement you made on the day and the facts of that day. You could either do this yourself, or ask a solicitor at a local law firm to assist you. The latter might be an attractive option even if you had no wish to allow it to be contested in Court - the solicitor would be well placed to attempt the negotiated settlement on your behalf in due course, if you felt you will lack the confidence to do it yourself, and they would be better placed to do so if they had been givent he opportunity to discuss it with you before you wrote back.
Only you will know if you want to incur legal costs - an initial interview would probably be free and might help you decide.
If you would rather reply without legal representation then that is fine. Don't at this stage take the bait of challenging the quality of their evidence against you (as others on here have suggested). There may be a time for that later, but at present, just stick to the facts.