I understand your frustrations, and without knowledge of your case, I am not replying directly. However, I work as a Customer Service Manager so can answer some general points. Without revealing any trade secrets!
We get many people who believe good customer service is giving them what they want. Whereas this is not the case. Generally companies will treat everyone equally. So anyone else who had the same problem will get the same treatment.
If you email the MD (or any other director) it will just be passed to the customer service team. Don't think the person you emailed will actually read the email. Although most companies have a team who (amongst other things) deal with these emails, but they will search for other correspondence from you, and merge them all together. It may, or may not, get a faster response depending on work load.
If the thing you are complaining about is contracted out to another company (for example car parking) then the company it is contracted out to, will usually deal with all the complaints as part of their contract. So it is best to deal with them directly. If you feel the company who contracted it out were in some way to blame, put that in the complaint to the contract company, and they will investigate with the company directly. They will have a direct contact, and get a much faster response. If the actual company (rather than the contractor) were at fault, they will then respond directly to you.
No company necessarily has to have an escalation process, as the front line staff can do everything. Otherwise, everyone would have to be a manager, and that rather defeats the point. It is best to offer what you feel the solution should be, and that gives them something to work with. But make it reasonable. Ultimately, the company lawyers will decide what the outcome would be if it went to court, and that will decide what, if anything, is done.
In the crudest terms, the cost of a lost customer who is unhappy at an outcome, will be less that what the car park brings in, so that could be viewed as the price that has to be paid. By all means fight it, but I wouldn't let it cost you any money. If I had had a £1 for everyone who said "I'll see you in court" I wouldn't need to work! However, very very few actually do. And you can rest assured the company will not let it get to court if they are not confident of victory. We have recently been to court with an unhappy customer, and we won. But they were determined to go to court over it. Goodness knows what it cost them!
In your case, I would certainly be approaching the car park contractor.