Whether or not you pay the charge is entirely down to you, how strongly you feel and how resilient you are prepared to be!
The ticket is a private ticket - you have committed no 'offence' broken no 'law' nor will you have the police knocking at the door. If you study the
sticky on the front page regarding private parking companies then you will learn that ultimately there is no legal obligation to pay this charge, although the parking company will probably make threats of escalating costs, court action and debt collection.
Understand one thing - if you send payment with your appeal then you will not see your money again! It is a near certainty that any 'appeal' will fail. What you have is an allegation that you have trespassed and UKCPS, acting on behalf of the landowner are willing to settle out of court for £60. However much they threaten, they will not take you to court as except in very limited circumstances the remedy for trespass is damages to the landowner in reflection of any loss caused by your trespass. Did the landowner lose financially or otherwise as a result of your action? Highly unlikely.
UKPCS are running a business - their own website states this as their 'revenue is from charges made to motorists'. In order to generate a (significant) profit they rely on people paying up, and futile civil action would simply be a cost with little chance of recovery.
Does the car park belong to the church? If so, you were there with the permission of the landowner (well certainly His representative!). If so then perhaps the Minister would be prepared to have the ticket cancelled for you.
Personally I would do nothing. UKPCS will then obtain the registered keeper's address from the DVLA and write demanding payment. At this point write back and refuse payment on the grounds that you were parked there with permission and made no agreement with either the landowner of UKPCS to pay for the privilege. You will probably then receive a letter from a debt collector threatening legal action, at which point you advise them that the matter is in dispute with their client. The matter may end at that point, but if not it will do another few circuits before UKPCS realise that the cost of the threats is outweighing the chance of receiving payment.
Plenty of people around to offer support and advice if you need it, but have a read around various threads (if you haven't already) and I can almost guarantee that you will not find a single case which has proceeded to enforcement.