If PE have a letter from the landowners giving them permission to administer charges on their land, then PE can invoice as they see fit. If they choose to chase you through the courts, then they could well get a result. Just because they choose not to in most cases, then does that mean you should still throw it in the bin?
Basically (and this is what it boils down to), it's people trying to get something for nothing. If you park on a bit of land and you know that you should be paying to park there, then cough up. Morally that's the right thing to do, whether you agree with those charges or not they're almost always in plain sight. In the case of the OP I do have a certain amount of sympathy, but still he could've checked for change and/or phone signal before parking. Not saying I would've done any different (I wouldn't), but the option is there. The OP could have gone and done his shopping, got some change, then come back and paid for a ticket for as long as he was there for. Yes, the bill still would've come through the door, but you would've had cast iron proof you paid for the amount of time you were there, albeit retrospectively.
FWIW, I've ignored a letter from them before too, albeit for one of my drivers rather than personally, so I don't claim to sit on the high horse without a flaw.