I am sorry but most of these answers are wrong.
Just because a company sends a letter to your old address does not mean that you have made contact. If you have not made any payments in 6 years or acknowledged the debt IN WRITING in 6 years then the debt is statute barred. They can write to you as many times as they like, this DOES NOT stop the debt becoming statute barred, ONLY you acknowledging the debt or paying before the 6 years is up will stop this.
A company can only keep a debt alive by getting a CCJ, sending letters will not keep a debt alive, and this does not reset the clock. Only MAKING A PAYMENT OR SENDING A LETTER SAYING THAT YOU DO OWE THE MONEY will reset the clock, other than a CCJ there is NOTHING a company can do to reset the clock.
Hammer - your answer is confusing. Once a debt reaches 6 years it is statute barred. But a creditor sending letters will not reset the clock (unless they get a CCJ).
The debt will always remain, the company just cannot take you to court and if they continue to harras then you can take steps to stop it happening.