Andy, the onus is on them to prove who parked the car there. DO NOT PAY!
Write to them, admit you are the registered keeper but say you cannot remember who was driving the car on that date. Ask them to provide evidence of who was driving. If they send a photo of you, then you will have to cough up. If they cannot provide evidence and then they still keep demanding money from them, write and say you do not want to hear from them again and if they persist, you will report them for harrassment.