Don't waste any time calling Action Fraud. Ridiculous suggestion.
The Council has powers to move vehicle where they need access for roadworks and the like - it's all legal and above board.
They will have records and photos of which vehicles were moved, where and when. I would expect under these circumstances that you will successfully get all the PCNs cancelled.
Write a clear, reasonable letter to the Council, explaining what happened on the day. Don't use words like fraud or profit, or approach them as if they are your mortal enemy - just explain the events, and that the council put your car there without your knowledge. The fact that you had so many PCNs and the council did not tow the car to the pound indicates they knew the situation anyway, but they won't consider cancelling and PCNs unless you appeal.