Penalty Charge Notices and Parking Charge Notices are not Fines
Only a Court of Record can issue Fines, and then only after due process. Councils and companies like Parking Eye do not issue Fines, they issue Charge Notices.
If we stop calling these Charge Notices 'Fines', we will be well on our way to freedom from mental slavery.
For every Notice of levy or charge you receive, you have the right to demand an invoice, this was enshrined in the Bills of Exchange Act in 1882 which has been the bedrock of business-to-business transactions ever since it was enacted.
Private individuals enjoy the same protection under the Act.
Companies are not obliged to offer you a properly formatted invoice in the first instance, but once you request one they must either comply or cancel their demands.
Many businesses will automatically generate a proper invoice when supplying goods or services to another business or to private individuals.
There are severe penalties for those who fail to comply with this requirement. Making repeated demands for payment without issuing a proper invoice when required can attract a custodial sentence of 7 years for minor employees and 10 years for company executives. It's right there in the Bills of Exchange Act, read it for yourself.
You stand to lose nothing by trying out this method; you are merely standing on your legal right to demand a proper invoice.
If those making the charges had any legitimate claim, they would be happy to send a properly-formatted invoice on which they account for VAT.
Stand in your own power.