it looks at this stage as though this will hinge on the wording of any letters from De Vere and the details of their claim (plus any letters you sent to them).
by all means scan or photograph their particulars of claim, scrub out your identifying details and post it up.
Some more details on the mediation would also be good, at the moment we don't really have the details or the full story.
e.g. do they call it a 'penalty', what did the sign(s) say - again pictures needed, their paper trail could well break statutes but we haven't seen it.
other questions as well but best kept off-board as a LOT of PPCs hang out here...
Is there is the a deadline date for any next step ? if so what is that date ?
In the meantime write to the DVLA and get all the information from the V888/2 request including the evidence of contract with the landowner.
see
How to request information from DVLA records : Directgov - Motoring
I can't find A Data protection register entry for them. PPC shave to provide a valid DP registration in the V888 request. this will help peel this onion. the 'evidence of contract' can lead to you finding out that they actually don't have any right to issue tickets. I bet they issued paper via MCOL and have not provided ANY proof to legal entitlement.
footnote Devere is 'normally' in fact TPS.