@BrilliantBetty We had this in a house we moved into some 11-12 years ago.
A previous occupier had left £25-30K of debt, with a number of institutions. Payday loan companies, banks, stores, and credit cards. We got loads of letters and 'visitors' for the first few weeks we were there. It was quite scary!
However, 'just leaving it' and sending stuff back with 'not known at this address' does not work. It won't stop. The letters will keep coming, and so will the bailiffs and debt collectors. We found that out! So we contacted them all about 6 weeks after moving in, (as nothing stopped when we ignored it all.) Sending stuff back - return to sender - and ignoring it all, didn't work.
When we worked with them, and helped them, and provided what we needed to, to prove we had only just moved in, it all stopped quite quickly.
It is very un-nerving, but as a pp said, if you contact these people/ institutions/ bailiffs, and explain you are a new owner, and you have only just moved in; they will do their own investigation, (with a little info from you,) and then they will leave you alone.
As a pp said, it can sometimes take a little longer if the company has sold the debt on, but the new company will leave you alone too, once you contact them and prove who you are, and that you only just moved in. Shouldn't take more than a month to sort it all out. Depending on how many creditors the debtor had of course!
Debt collectors/bailiffs are a bit scary and intimidating, but they're not monsters, and they're mostly OK.
Just contact them all, and work with them, (the people calling at your house AND the people writing to you,) and this will all resolve itself.