Dont respond to letters as they will then know who was driving the vehicle,
Write to them telling them that,as they have not provided any evidence of a contract being entered into or broken, and that if there is such evidence then their dispute is with the driver of the car at the time and that that driver may or may not have been you. As a result, you have decided to decline their kind offer to allow you give them some money they are not entitled to. However, being a reasonable sort of chap, you are prepared to allow an appeal at a cost of £250 regardless of the outcome. Any further communication from them, other than an indication of no further action or communication from them, shall be treated as an appeal and subject to the appeal charge. Any appeal not accompanied by the relevant payment shall be rejected out of hand, but shall still be subject to the appeal charge. No discussion will be entered into regarding the decision of the appeal process. Should the parking operators seek to engage in further communication, such communication shall be returned to them, at their cost, incurring an administrative cost of £25 per returned communication.
That should shut them up, it works for me.