They won't though will they? I didn't think these private companies ever accepted an appeal. As far as they're concerned if they accept your appeal they'll get no money. If they reject your appeal, they might get some money. They're not interested in the rights and wrongs of it.
Regardless of blame, £100 for a parking charge is just criminal. Is there no limit to what they can charge? I mean - can they make it $1000 if they want to?