Addresses are not blacklisted, so if you are struggling to obtain credit, it will be based on your own circumstances and not those of previous occupants, etc.
You need to obtain a copy of your credit file, so you can see exactly what the lenders are seeing when they consider any applications from you.
The two main credit reference agencies are Experian and Equifax, and you can apply online for a copy of your report at
http://www.experian.co.uk and
http://www.equifax.co.uk. There is a small fee to pay.
Not all lenders use both credit reference agencies, so you may find that some information appears on one report but not on the other. If you can't understand why you might have a poor credit rating / why you are struggling to obtain credit, it might be worth forking out for both reports, to make sure there is no inaccurate information on either.