People don't get blacklisted. Neither do addresses. This ended a long time ago.
Who do you owe the money too? If it's a bank/credit card etc, they will mark down your inability to pay on your credit rating. This will make getting any other credit difficult - things like overdrafts, credit cards, loans, rental agreements, phone contracts etc.
Your student loan is not credit-checked, so you will still get it. Your bank account should be fine too, unless you have a loan/credit card with the same bank, in which case you should move accounts. You'll be able to get a basic account, with no credit card or overdraft, even if you have bad credit.
It's worth noting that you are unlikely to get a student overdraft if you have bad credit, and if you already have one, they could remove it. It might be worth asking your parents or friends for help paying it off rather than trying to manage without the overdraft.