Technically the car does not belong to you, nor the previous "owner" but belongs to the finance company.
If you want to keep it to use yourself or to sell, the only thing you can do is contact the finance company and ask them if they will allow you to pay off the remaining finance.
If you think it is not worth the amount it would cost to do pay off, then you can give the car back to the finance company- because the finance agreement is in the other parties name, they will be liable for any outstanding debt, but you wont get the car or any money back.
Thats why you have to do an HPI check before buying a used car. It might cost �25 odd pounds, but as you have discovered, it is more costly not to!