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Went in, agreed a part ex, was going to pay up front, they wanted to do a credit agreement. I said it was too costly, they insisted on showing the maths. Once they did, I calculated the interest cost to me of paying in three installments as £2.40 IN TOTAL. I informed them they'd made a mistake, said that can't possibly be correct, it's far too cheap. They insisted that no, their new finance deal really was that good. I signed up and decided to do a flexible overpay on the mortgage until the money was due, saved a few £. A week after we took delivery, their finance guy called us and said 'we made a mistake, we're out by a factor of 100 on the interest charge, it should actually be £240. We said no way, they asked us to pay the lump instead, we held our ground, said no and indicated we'd complain to the financial services ombudsman if they insisted. They dropped it.

Difference was we actually had the car by the time they changed their minds so had a bit more power. I seem to recall saying if we can't agree then your recourse is to take the car back and refund us in full - which they clearly wouldn't want to do due to depreciation due to extra owner and extra miles.

I'd suggest letting them know how unhappy you are, that you're prepared to walk away, you will be leaving honest reviews, etc. They're hopefully willing to write off their perceived loss for the good will and to avoid negative publicity.

As for the legal framework - no idea, but easier if you can bring them around to a 'customer is always right' way of thinking.