Did you finally pay off the loan in full? If so, you should make a request to them for the information they hold on you, under the Data Protection Act. You can seek to have any material errors corrected (if they state you are still a debtor, for example). That might make them reconsider, assuming you're still interested in opening an account with them.
If, however, you made an agreement to pay a reduced amount and didn't actually clear the full loan amount you may be down in their records as a bad debt on which they had to write off part of the loan - and it's understandable, though rather frustrating, that they'd be unwilling to deal with you again.