Does a debt ever go away? Or can they chase you for payment years after the event?

Have you checked your credit files?
They may have registered a default which would have a serious impact on any mortgage application.

Agreed, check your credit files too. You can do this on:
www.creditexpert.co.uk
www.equifax.co.uk >>>> (edited: experian is the same as creditexpert, D'OH)
www.callcredit.co.uk
These are the 3 main agencies used by the majority of companise. The top two offer a free 30 day trial, as long as you cancel within then they dont charge your card.

Maybe Talk Talk have just twigged that they have 2 sets of details, either that or they sold of a batch of old debt. I dont know whether they would seriously consider taking you to court for £200 though. Your saving grace may also be that as its with a DCA (which one btw?) they will probably freeze interest and charges.

Best advice is, once you have all information, try and enter into a repayment plan. And never, ever talk to them on the phone, they are known to use bully and scare tactics. Always correspond in writing, and dont sign the letters.