From the sounds of it somebody has told you that if you have has previous tenants / owners with bad credit - this will affect you!
Well the truth is as far as credit reference agencies go - there is NO such thing as a blacklist. --- fact (ref:- experian.co.uk)
What they do check for is your SURNAME + POSTCODE. (Now if these match-then you might need to clarify that you are ABC XYZ and not CAB XYZ - if this is affecting your credit file. Again this is VERY VERY unlikely)
On the other hand if YOU jave bad debit - then....that's a different ball-game.
Finally - you aint got to clear anyones debt. - You aint there fairy god father/mother are you???
Easy enough. You go online or contact the relevant agencies (usually Experian or Equifax - and download/request a Notice of Disassociation. List the names of the people you want removed from your credit register, sign the disclaimer and that should be enough.
Occasionally, there might be a query, but it's unlikely.