I received a parking charge notice in my wife’s car.
Did you, or did your wife? I don't ask this purely to be pedantic - if the notice is addressed to her, then it is her who Civil Enforcement will be pursuing, and any appeals etc. will need to be in her name.
Can you please also show us the rear of the notice?
Your first step, if you haven't already, is to speak to the managers of the restaurant to ask them to intervene.