Can I argue I never left, that my car could still be there, or that I just don't believe this is me?
Before we get onto any avenues of defence, anything you argue in court must be truthful, unless you fancy committing perjury and turning a £100 parking charge into a potential prison sentence.
Likewise, lying in writing in a bid to ward off the parking company is equally unwise - if you do this and the matter goes to court and it becomes apparrent you have been less than truthful, the judge is unlikely to believe anything you subsequently say.
So, what you can argue will depend on the facts of the case. You may well have decent avenues of defence, but first we need to get more information on the table. Take a look at the following thread, and provide as much of the information it asks for as you are able to:
READ THIS FIRST - Private Parking Charges Forum guide