Hi red,
Don't worry. The mortgage is for you and will be based on your credit history. The address isn't blacklisted, just the previous owners.
We bought this house without knowing the extent of the 2 previous occupiers owing thousands and thousands to banks and credit cards and catalogues.
The occasional letters still come through, we have stopped the post office delivering to this address in those previous names and they just RTS them.
Go to the post office and stop post coming to your address in their name.
Best o'luck on your new adventures with housey buying :)