You can get a post office account, they are designed for people who cannot get a normal account, you can have wages etc paid into them but cannot arrange DDs on them and have to use cash rather than a card. Using things like that will help you gradually improve your rating.
I have a Barcleys basic account since going bankrupt. I have a card for withdrawing out of certain machines plus can do direct debits. Can't go overdrawn/have an overdraft, cheque book or switch type card. But none of those matter to me.
I work for Abbey (don't flame me its by defualt) and we have basic account that you should be able to get (no overdraft) but you do get hol ein wall card and can set up direct debits and standing orders
oh yea Tesco is the only pita - had no problem with Ocado or Asda online though, (or anywhere else for that matter, bought traintickets and all sorts on-line with my Visa Electron - just Tesco doesn't like it)
I use think bank. It is really good, you basically have two bank accounts, one where your wages are paid in and it automatically keeps back what you need for your bills, and then it automatically transfers your "spends" on to an account with a card. You can use the card in shops or cash machines as well as online.
It does cost £12.50 a month, but there are no other charges, and as I was spending about £60 a month on banks charges from forgetting to leave enough in for bills, that is a massive saving for me.
Absolutely no credit checks or anything, but obviously no overdraft either.