It's presumably not a real "Penalty Charge Notice" from a council but from a private contractor?
The key thing to remember is that they have written to you as registered keeper of the car, and they will argue that you have entered a contract to park your car, and breached it by staying too long, etc.
That contract, if it existed, was with the driver of the car, not the registered keeper, so firstly, don't admit to having been the driver. If they can't prove who the driver was, it's not legally enforceable.
Many people get away with these simply by ignoring EVERY communication. They will get increasingly aggressive, threatening court action, etc but the fact is they can't initiate court action without you naming the driver, and it would probably cost them too much for it to be worth their while in any case.
However, in this case you have a valid reason for appeal, and, faced with 11 notices, they might start to consider it worth taking legal action if you simply ignore everything.
I would therefore write to them as the registered keeper of the car indicating that the car was used during the period of the PCNs by an employee of the site (do not indicate that you were the employee) with the permission of the toy store manager (name the manager(s) if you think it would help).
Then say that you trust that this has been a mistake and that you will not enter into any further communication on the matter.
You have not indicated that you were the driver (could be a family member or previous owner). Tell the truth, but only divulge the information that will help you, not that which will help them.
I would then ignore anything else, by phone or letter. If you start to get pestered too much then you could write accusing them of harassment but see how it goes first.
Paying can be seen as an admission of guilt, so don't pay and then hope to claim it back!
Keep copies of all correspondence and anything that could prove you worked on the site and had permission to park there (parking permits, pay slips, etc.)
Note: I'm not qualified to offer legal advice; just stating what my response would be.
It's well worth reading the links to moneysavingexpert and also look at the advice on pepipoo.
Kevin