I've been advised to plead guilty, accept the fine and take the person who's responsible for this to court privately to recoup damages.
Terrible advice but from the way you've written it, you seem to suggest you know who the other person is.
Well is it linked to that thread?
I would have thought someone in your situation would immediately check what they were doing on the said date at the said time. Where were you? Who was with you? Were you at college, work, etc. Is it a train route you normally use or never use? How long ago did you move to the new address? You weren't by chance on the same train at the same time and a friend who you know gave your addresses were you? That would be really bad luck.