Indeed I have. MFG is the parent company and unfortunately have outsourced their customer service team to India. Let's just say the level of service is below par and they kept deferring me to Euro Car Parks, as they are unable to assist with the matter.
Maybe some of these guys would be able to help...
https://www.motorfuelgroup.com/leadership-team/There is no sign on the jet wash to indicate that time can be extended by giving your registration in-store. There may be signs elsewhere, but I would argue they can easily be overlooked, as they are not in the most obvious of places.
Are you sure? Page 4 of the first rejection and Page 3 of the second rejection show a sign which seems to be affixed to the 'glass panel' the typically surrounds a jet wash bay.
To be clear, I'm not meaning to be argumentative but you will need to be very clear on all of the circumstances in the instance this ends up in court. For example, if they're showing an picture from a different site the court would take a dim view, but if you say there isn't/wasn't one and its provable there was, that will also be a problem.
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I would agree that it looks like they are willing to accept it as a keying error - but since there wasn't a keying error that would seem odd and I wouldn't simply take them at their word. If the online portal now also shows £20 I guess you'd probably be fine.
That said if there was a keying error by the attendant in the store (since it doesn't sound like a self serve situation) then how could you possibly be on the hook for any amount of money? The BPA guidance also says up to £20 for admin costs, I wonder if it really cost them £20 to reply to a couple of appeals with boilerplate/inaccurate letters? Their willingness to drop the cost would seem like they're clutching at straws to get something out of you.
You have a choice - accept the mugs discount - or fight them all the way for what is clearly an unreasonable charge.