If the debt is an ordinary one (i.e. not secured on a property) and you have not made any payment on it or acknowledged that you owe it for the last 6 years, then it is statute barred. This means the creditor cannot take legal action to enforce payment, but the debt still exists and can still adversely affect your credit rating. The exceptions to this are if the debt is a joint one with someone else who has made payment, or if the creditor obtained a County Court Judgement before the 6 years was up.
You do not have to prove that you have not heard anything; they have to prove the debt can still be enforced or any Court would refuse to grant a judgement.
Many people in these circumstances arrange for a full and final settlement at a fraction of the full debt amount to be made (this should be done through a third party and not by the debtor) to clear the debt once and for all; otherwise repreated contact can be made by different debt collectors over the years. However, the first thing is to get them to agree that the debt is statute barred, so you could write to them saying this is the case and see what their response is. Alternatively, you could ignore it and see whether they do anything further.