Free Traffic Legal Advice

Afternoon, I’m hoping someone can please advise.
I bought a car from a friend last year. I paid a cash deposit in September and arranged insurance for my family. In December, I paid the remaining balance and the vehicle tax, and everything was completed.
On 29 January, a bailiff clamped my car outside my home, stating there was an outstanding PCN linked to the vehicle. I explained that I only purchased the car recently and showed the V5C, but I was told that the V5C is not proof of ownership. I was forced to pay £560 to have the clamp removed because the vehicle would otherwise be towed. The bailiff briefly mentioned that I could make a claim but didn’t explain how. He also gave me a receipt containing the full name and address of the previous owner.
I raised a complaint and referenced the relevant laws, but it was rejected. I sent them a copy of the agreement from September stating the V5C would not be released until the full payment was made. I also provided the tax payment receipt and the bank transfer shown on my statement, but they said bank statement did not prove the documents were genuine.
To complicate matters, the name of the person I bought the car from is different to the name on the V5C, which I did not know at the time.
I have requested the PCN and council details, but they refused to provide them. I’ve also asked my friend to prepare a sale receipt, but I’m worried it will be rejected because it isn’t on headed paper—it was a private sale, so I don’t see how it could be on headed paper anyway.
I can share my email correspondence and the bailiff’s response if needed.
Please advise what my next steps should be.

You should have let them tow the car and then claimed it was unlawfully towed on the ground that it is your car and you are not the debtor, to be honest it is unlikely they would have towed it because in such circumstances the creditor (i.e. the council) has to pay the costs of towing and storing the vehicle up-front and if it turns out that they paid for the wrong vehicle to be towed, the council would throw that money down the drain and have nothing to show for it. In practice it is far more likely the bailiff would have left the clamp on for a few days in the hope that the threat of towing would scare you into paying, and when that didn't work he would have taken the clamp off and you wouldn't have heard anything further.

Because you've paid, it may well be that you are considered to have made payment as an agent of the judgment debtor, so strictly speaking your recourse would be to sue the actual recipient of the PCN to try and recover the money from him.

The other obstacle you face is that due to the PCN not being in your name, nobody will give you any details because of GDPR, as the debt is nothing to do with you.

In summary, I think you'll have to sue the previous owner of the car.