The onus is on them to prove that you owe the debt - which, under the circumstances they are going to be hard pushed to do.
I MIGHT BE WRONG IN SUGGESTING THIS AND I HOPE SOMEBODY ELSE WILL ADVISE YOU FURTHER VERY SOON...................
I would send them a CCA request, letter N here
Creditors and DCAs - Letter Templates & Budget Planner UNDER NO CIRCUMSTANCES SIGN ANYTHING YOU SEND ! Enclose a £1 postal order with the letter and send it either by recorded or special delivery and keep your receipts. They have 12+2 days to comply with the request and then the debt is officially in dispute.
Have you spoken to the credit card company direct to explain the situation? It looks as though who ever moved into the property after you had left has used your husbands name. Can you prove that you had nothing to do with the property when the card was taken out? ie, claims for housing/council tax benefit, tenancy agreement, proof of sale of the house etc.
Can I ask how much they say you owe and to what credit card company?
If they phone you, refuse to speak to them and tell them everything MUST be in writing.
Keep everything they send you and a copy of everything you send them.