I have an account with the abbey which was / is a current account, which last year I asked them to convert the card to an electron card so that I could pay for Ryanair flights without paying a massive booking fee (as I visit family in Ireland).
Simple bank accounts and the electron card which only offer debit and not credit services (so not a 'current account') are aimed at people with bad credit or difficulty, and so you should be able to get this account.
You can use an electron card online, and do electronic transfers (and online banking) with the account that I have. There are some places that won't accept an electron card, but this should be infrequent.
There are no charges from the Abbey for using the card, but you still might be charged at some ATMs (that charge everybody)
You might be able to apply online, but you would still have to prove your identity and address at a branch, so it might be worth going in anyway and make an appointment to see someone.
Good Luck with it, and the sooner you are away from the rip off money shop the better!
Sparky