Car Bought with Outstanding Finance

If the car turns out to have outstanding finance, a private buyer who bought in good faith, without knowing about it, may be able to keep it (conditions apply, e.g. being the first private buyer); otherwise seek a refund from the seller (CRA 2015 if a trader, Sale of Goods Act 1979 if private). source

Private sales: you have fewer rights than when you buy from a trader. The car must be as described and the seller must own it (have good title), but it does not have to be of satisfactory quality or fit for purpose unless the seller said so. Some traders pose as private sellers to avoid their legal obligations; report this to Citizens Advice. source

Section 75 Consumer Credit Act: if you pay by credit card (or buy now, pay later) for an item costing over 100 pounds and up to 30,000 pounds you can claim from the card provider for breach of contract or misrepresentation even if only part was paid by card; chargeback may help with debit cards. Escalate to the Financial Ombudsman Service if refused. source