It is possible for you to prove and it’s possible for them to prove that they sold you a car (they did sell you a car) but it is impossible for you to prove that they didn’t.
The bank have acted completely unreasonably.
They had no right to block your account simply based upon someone else’s say-so unless someone else had a court order or the person that lent you the money paid you by debit card (withdrawing the money on debit card is different than paying by debit card)
There is no legal aid for the action you are planning.Unless you want to spend and risk lots more money going to court, which could cost thousands of pounds in legal costs because the bank will defend your action, I would suggest that you might want to complain to the Financial Ombudsman Service which is cost and risk free.
You have to exhausted the bank’s internal complaints procedure.
Can I clarify anything for you?
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