You almost certainly can't stop the mail. The bank has a contractual duty to its customers to send statements to the last address notified to the bank. Until such time as your step-daughter (and nobody else) notifies the bank of a new address (to which statements should be sent), the bank is legally obliged to continue sending them to your address.
Credit reference agencies are not permitted to blacklist people based solely upon their address. However they can do so where they believe that a financial 'association' (such as a family relationship) exists between the debtor and the householder. If you believe that might occur in your circumstances, you should file a 'notice of disassociation' with at least one of the main credit reference agencies. (They normally share such information with each other so, theoretically at least, you should only need to do so with one agency).
Contact details for the three main UK credit reference agencies are here:
http://www.ico.gov.uk...ic_guides/credit.aspx
Chris