The UK Police issue Fixed Penalty Notices, The Gardai issue Fixed Charge Notices, Traffic Wardens are also permitted issue them for certain offences.
The Gardai & Wardens are entitled to issued FCNs for an offence on private property to which the public are admitted as set out in the Road Traffic & Local Authority (Traffic Wardens) Acts. You do something stupid in a private business's car park, you can be done for it, the property owner does not get a say.
Unless you decide to be a lot less cryptic, there's little more to be gained here.