I would suggest that before you do anything you enquire about your credit "rating" rather than speculating that "I shouldn't have any bad credit history".
On a personal basis, I have a Premier Direct account, which I opened in 2006. They gave me an overdraft and the credit card both of which were ample for my needs. Having kept an eye on comments on the account over the years it is my understanding that you would be unlikely to improve the terms they have offered/imposed on you as at square one.