I`ve looked into it this morning, and they can take you to court,
From here -
About ParkingEye parking tickets | Parking Cowboys
"Ignoring private parking tickets was the popular advice until late 2012. Before then, threatening letters would be sent for months after the ticket, but in the end, they would just stop when the parking company realised the recipient would not ‘bite’. However, as noted earlier Parking Eye has started a campaign to change that perception by issuing court claims. Parking Eye could not realistically issue a claim for every ignored ticket; there would be too many, and it would cost them too much (NB. for cases that reach court, Parking Eye lose money on solicitors costs even if they win the case). However, if you do ignore a ParkingEye ticket, you could well be one of the unlucky ones."
I received one this morning, been round to reception and since I was there playing football at the time, the charge will be cancelled. Thought it worth a mention for others to avoid the aggro.