My own two pennorth, for what it is worth, is that in reality the only difference between, say, a Cashminder and a so called "normal" account is that a normal account offers more in the way of credit facilities. Whether that be by way of overdraft, credit card, loan or even a cheque book, which can still be a means of credit if used correctly and cleverly, would be down to the bank itself. Now, if you are, in your own opinion, rehabilitated and ready to get back on the credit bus again, as it were, then fair enough, if a bank will let you. For the life of me I see no advantage to them at all if you are not wanting credit facilities though.
I run a Cashminder personally, and I swear by it. It doesn't give me a cheque book, which is fine as I have no use for one and who accepts cheques now anyway in reality now that the cheque guarantee scheme has ended? Direct debits, standing orders, phone banking, internet banking and a debit card (not Electron) that can be used anywhere in the world. Further, in over 3 years they have NEVER contacted me in order to try and sell me something, whether by phone or even letter. I have never paid 1 penny piece for the privilege either. It is to be remembered that "normal" accounts carry hefty monthly fees in the majority of cases so I have to repeat that I will be the last in the queue to line the pockets of our honourable friends the banking community I'm afraid.
Regards.