The law you refer to does not exist. This is because responsibility for a debt is not affected by whether or not someone is married, and marriage in itself does not create liability.
What is relevant is whose name is on the agreement, as this is the person who will be legally liable for the debt. Therefore, a husband is not responsible for his wife's debts, or vice versa, if his name is not on the original credit agreement.
In this case you do not say whether the debt is in joint names. If it is, you have what is known as 'joint and several liability'. This means that until the debt is cleared in full, each party is individually liable for the whole remaining balance of the debt, so a creditor can pursue either, or both parties for this.
Alternatively, if a joint debt does exist, one party's liability can be ended through bankruptcy, an IVA, or sometimes through an agreed settlement with the creditor.
In terms of credit referencing, a financial link would be created with another person if there is a joint bank or credit account or there has been a joint application for credit. If you are financially linked to another person, then lenders are allowed to take both your credit histories into account when either of you apply for credit, because they see you as one financial unit and the credit of one would impact on the other. The credit history of anyone you're linked to is not shown on your credit report, but their name will be listed as an 'associate' .
Regardless of whether they are related to you, if you have no financial links to an individual their credit history will not affect yours in any way. It is probably worthwhile obtaining a copy of your credit reference file to see if you are financially linked to another person. If you are, but there are no longer any joint accounts or credit debts, then contact the credit reference agency who can arrange for the link to be removed.
However if there is a financial link, which cannot be severed, then a Notice of Correction is something you may wish to consider. This is a short note of up to 200 words that you can add to your credit report to explain the background to the information held there.
Anyone searching your report in the future or who has seen it in the previous six months will see the Notice of Correction, and they must take account of it, if and when you apply for credit.
Sources: http://www.thisismoney.co.uk/ask-an-
expert/loans/article.html?in_article_id=452971&in_page_id=110
