Credit reference agencies are not permitted to base their checks solely upon addresses. (Otherwise, for example, you might be given a poor credit rating simply because you moved into a house previously occupied by someone with financial problems). They are, however, entitled to link you to another person with whom they believe you may have had a financial association.
For example, if Fred Bloggs moves into a house after Ada Smith leaves, their credit records can't be linked. However, if Fred Bloggs and Ada Smith cohabit at the same address, the credit reference agency have the right (in the absence of contradictory evidence) to assume that their finances are linked. If you believe that a credit reference agency has unfairly linked your credit status to that of another person (or if they did so fairly but there are now no longer any financial ties between you and the other person), you can file a 'notice of disassociation' with one of the main credit reference agencies. (This information is automatically passed on to the other agencies).
To do this, go here:
http://www.experian.co.uk/consumer/index.html
Click 'Questions', then 'About Your Credit Report', then 'Other People', then choose the appropriate link for the online or postal method of filing the notice.
Chris