I'd be extremely surprised if either you or your former partner actually owe any money to DFS. It's far more likely that the debt is with an independent finance company.
When you make a purchase like this, what normally happens is that the salesman has two roles. Firstly, he's selling you a suite on behalf of DFS. Secondly, he's acting as an agent for an independent finance company. By the time you've left the store, two things will have happened. The first of these is that the salesman will have arranged a loan for you with the finance company. (This is exactly the same as if he walked up the road to a bank and persuaded them to give you a loan. i.e. you owe the money to the lender, not to DFS). Then the salesman will use the money you've just been loaned to pay for the suite which you purchase from DFS.
From that moment on, you own the suite outright (i.e. it can't be repossessed), DFS have got all of their money (paid for from the loan) and you owe money to the finance company (and not to DFS).
However, when I wrote 'you' in the previous paragraph, I should really have written 'the purchaser'. The debt to the finance company lies with the person who signed the contract. As I understand it, this was your former partner and not yourself. That means that you don't owe anyone anything. You should contact the lender (via DFS if you haven't got the direct contact details) to advise them of your ex-partner's new address. You should also contact your ex-partner to remind him that he is the (outright) legal owner of the suite and that he may collect it from you if he wishes to do so.
Lastly, so that your own credit rating isn't affected by your ex-partner's debt, you should file a 'notice of disassociation' with one of the three main credit reference agencies. (They will forward it to the other two agencies). Phone Experian on 0800 656 9000 to find out how to do this.
Chris