Even if you admitted that they were the driver then you can claim that the penalty is an unfair term in a consumer contract.
Last time I got a private ticket for overstaying my welcome at a supermarket car park (while I was shopping in the supermarket

) I sent something similar to the following:
Furthermore, and in the alternative, even if a contract were to exist with the driver of the vehicle (which is denied) the charges would amount to an unfair term in a consumer contract as per the Unfair Terms in Consumer Contract regulations [Statutory Instrument 1999 No. 2083], Unfair Contract Terms Act [1977], and common law.
I refer you to the cases of:
• Lord Elphinstone v. Monkland Iron and Coal Co [1886]
• Wilson v. Love [1896]
• Castaneda and Others v. Clydebank Engineering and Shipbuilding Co., Ltd. [1904] 12 SLT 498
• Commissioner of Public Works v Hills [1906] AC 368
• Campbell Discount Co Ltd v Bridge [1962] AC 600
• Philips v The Attorney General of Hong Kong [1993] 61 BLR 41
• Murray v. Leisureplay (2004)
• First Commercial Bank and Others v. the Owners of "Mandarin Container", "Kingdom Container" and "Liberty Container" (2004).
Every time they sent me a letter I sent the same thing back. Couple of months later and they appear to have given up
