Can a past tenant’s debts affect a new tenant’s credit rating?

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My tenants opened a letter addressed to ‘The Business Owner’ which was a Google marketing circular to a past tenant who had run a series of hopeless business ventures from the house. As some digging by the new tenants revealed, there is some out-of-date business and marketing info linked to the address. The tenants are worried this could affect their credit rating and imply I should make efforts to ‘cleanse’ the house’s digital detritus. I’ve said I didn’t think it matters as names are different and most rental houses must have old info like this linked to them.

What the current tenants don’t know is that the past tenant also ran up huge debts with everyone then did a runner… we lost five months rent, bailiffs turned up, even the window cleaner was owed £70, and three years on debt collection agencies still write to the house. Some of the tenant’s financial shenanigans may even have been fraudulent. So; do the existing tenants ‘old info’ worries have any validity, and more significantly, could the previous tenant’s dodgy financial activity actually be a problem for us or new tenants, and if so what steps could I take?