Talk to citizens advice first. I had a similar problem where I needed to claim ownership of goods that baliffs wanted to remove (for someone elses debt) and all I needed was a solicitors letter with the disputed assets listed. They helped me out in minutes.
If you can, sue the baliffs, they have acted in a totally irresponsible manor. DVLA's records will clearly show that at the time that the tickets were issued the vehicle belonged to the previous owner. Under the circumstances and evidence as provided the baliffs should have secured the vehicle and then carried out further investigations before proceeding further. I'm no legal expert but I would believe the fines belong to the previous owner and not the vehicle and as such the baliffs had no right touching your property.
If it turns out you can sue I'd also make an official complaint to the appropriate regulating body.