It is very likely it is statute barred. This will be the case unless you made any payment or otherwise acknowledged that you owe the money within the last 6 years. The exception to this is if the creditor got a County Court Judgement before the 6 years was up, in which case the debt is never statute barred.
You do not have to prove to them that you paid. They have to prove that you owe the money and that it is not statute barred. If they take you to Court (highly unlikely) they would have to produce papers to the judge to prove this, because your defence to their claim would be that you did not owe any money and it was paid off over 6 years ago. Put this in writing to them by recorded delivery, and keep a copy. Do not be bullied into paying them anything unless you become satisfied that you did not pay off this debt.