I assume you are in England or Wales. The statute of limitations is 6 years. What this means is that Court action cannot be taken to enforce the debt if no payment has been made and the debt has not been acknowledged for 6 years. The exception is if a County Court Judgement has been obtained before the 6 years is up.
But the debt still exists, & they can go on chasing you for it. In a lot of cases they don't bother to when you tell them it is statute barred, but it is possible for them (or another debt recovery co.) to bring it up again at any time in the future. Also, they can muck up your credit reference records by putting info about the debt on there.