It would be useful to see some photos of the signage at the site, detailing the terms and conditions. In particular, it would be useful to know if this is a 'pay on entry' or 'pay before exit' car park?
If it is 'pay on entry', an argument around the broken machine(s) will be harder to make - the parking company will say that a broken machine doesn't mean that you are allowed to park for free, that when the driver was unable to pay he should have left, and by remaining he has agreed to pay £100 as detailed on the signage. If 'pay before exit', there may be more mileage in the argument.
No permit.
The charge doesn't seem to have anything to do with a permit? It says (backed up by your story) that the charge was issued for failing to pay.
This is in excess of Annex C: Permissible maximum parking charges and mandatory discounts - Standalone private car park or publicly accessible customer car park as stated on the GOV.UK website.
I assume you got this from the Private Parking Code of Practice
HERE? If so, the most important part of that code of practice is to be found at the very top of the page:
This guidance was withdrawn on 7 June 2022 - Private Parking Code of Practice is temporarily withdrawn pending review of the levels of private parking charges and additional fees.
Until that review happens, that code is not in force.
