You are quite correct in thinking a debt is the responsibility of the person or persons who obtained the loan, not the property, but it sometimes happens that moving into a property where the previous occupiers had debts causes problems, not least the amount of mail and perhaps unwelcome callers. The address should not be the reason for being unable to obtain a bank loan, remember no one has the right to demand a loan it is up to the lender. If your tenants believe incorrect information is being held they can obtain a copy of their credit reference file from the reference agency, there are three and the cost to obtain a copy of their file is £2 to each agency, which are Callcredit, Experian & Equifax.