Well.. you've already made the mistake of taking blame / responsibility for the accident... why would you do such a thing unless you were sure you'd caused the damage in the first place ? Most people won't, and don't, admit to an accident that is their fault, let alone admitting to one they didn't know they'd had !... is there damage on to your vehicle to indicate that it came into contact with theirs ?
Now you've admitted causing the damage, I don't see that you can get out of paying for it.... I wish I met more people like you on a day-to-day basis.. I don't think I could help myself in exploiting such situations...
However, it is extremely unlikely you will be prosecuted for this, given the circumstances. The police would have to demonstrate 'beyond reasonable doubt' that you were aware of an accident taking place and that, in the case of driving without due care and attention, that you were in fact driving without due care and attention. As you describe the situation in the car park, I don't think its likely they could suggest that.
In addition, the question needs to be asked 'if the other driver is claiming to have approached you about the accident, an approach that wasn't witnessed by the 3rd party, then what is the other driver claiming happened during that approach ?'.... that you refused to exchange details, that you ignored them... ?..... by asking this question, you could expose the other driver as a liar, and that would cast doubt on their entire claim...
This might be worth fighting through your own insurance company... particularly if you have protected no claims and/or legal cover...