Solo is, as far as I know, a debit/cash card. However, it is not as widely accepted as some, a bit like Electron. I have only been with Think Banking a month, but so far I have found it very good. They do charge £12.50 per month, but they do not charge if they return a direct debit. There are two accounts. You salary and other income is paid into the salary account, an amount is held back for your monthly regular payments, which you tell them about at the beginning, and the rest goes straight on to the card account. You are given a Maestro card, which is acceptable almost anywhere. Any extra money you pay in goes on to your card account too. So there is always enough money to pay your bills. Also they have online banking, on which debits appear immediately. If I use my card in the shop round the corner, come straight home, it is already showing. Other banks deduct the money, but you don't know where it has gone for at least two days.
You can also sign up for their text messaging service, which is free, and you get a text every time money is paid into your account. The only drawback is that you have to phone and tell them when a new debit is being set up and you can't cancel direct debits online.
There are lots of banks doing basic accounts, but they usually give you Solo or Electron or even just a cash card. They also still charge for returned debits and overdraft charges.
Think is run by the Royal Bank of Scotland and they do not do a credit check. All you need is proof of identity.