Yes they can still pursue for the debt, BUT, if you have not made a payment or have made any correspondance in writing for 6 years then the debt is unenforceable as it is statute barred.
However, if a CCJ is in place they can go back to court to enforce the CCJ and you will have to pay. But if there is no CCJ in place and you have not paid or written in 6 years they cannot get a CCJ so they cannot enforce the debt.
You need to send them a statute barred letter. They will still pursue you and write to you, but in a nutshell - No CCJ, No money!