So I just checked my credit score for the first time, and my Barclays and Yorkshire Bank current accounts are coming up as credit accounts (it does say current account, but says they also give me credit ) , even though I don’t have an overdraft on any of them? Is this normal?
It is normal. If you have a Current Account, you have the potential to have credit. Arranged credit (approved overdraft) or un-arranged credit (unapproved overdraft).
Banks are just reflecting that you have a bank account with the possibility of having some form of credit. They mark down your credit use as £0 each month until, well, you use credit. If you never do, it will always stay at £0 credit used.