It can go a couple of ways with ParkingEye. Sometimes they farm it out to a debt collector who will send a bunch of scary sounding letters before you eventually receive a Letter of Claim. Other times they do the litigation themselves.
Either way, you're looking out for a Letter of Claim, at which point you should come back here for advice.
They have up to 6 years from the date of parking to make a claim, but it would be unusual for ParkingEye to take that long, they're normally comparatively quick if they do decide to sue. If you move house before the matter has been to court, and before the 6 years have expired, write to them to provide your new address for service.
Thank you for the advice!
The debt collector letters are always fun for their creative use of the English language to make possible outcomes sound like the only outcome!
I shall wait for the Letter of Claim and come back here with any further updates.
Very much appreciated!