All banks have to offer a basic current account
with no credit check, it's something to do with old biddies' pensions not being paid over the counter at the Post Office any more. The basic account has to have an ATM/debit card and the facility for wages and benefits to be paid in and standing orders and direct debits to be paid out. What's more it doesn't need any money depositing to open it.

My credit rating is quite likely worse than yours (the only difference is that mine is my fault), a quick look at the Basic Bank Account thread on moneysupermarket.com showed that Yorkshire Bank and Clydesdale Bank were the two best options, as their current accounts come with a Maestro debit card, as opposed to a Solo or Electron which aren't accepted anywhere.

I applied for a Yorkshire Bank Readycash account two months ago, and was accepted without question. They do do a voter's roll search, but this is not a credit check, it's simply to confirm that a person with your name lives at the address on your driving licence/phone bill/other ID. They opened the account and gave me my account number immediately and I can confirm that the account does everything they said it would do.

(It's probably a good idea for you to avoid Clydesdale as they are part of the same group as Barclays, and technically if you put money in a Clydesdale account they could offset it against the Barclays debt. Cunts.)
(WillI'mNot logs in twice a year, every year, Sat 18 Jul 2009, 16:41, 1 reply)

Good stuff on BBAs
...except that Clydesdale is owned by National Australia Bank, who've got nothing to do with Barclays, so Soaps is safe with them.
(stalinism, Sat 18 Jul 2009, 18:18, closed)

I stand corrected
tbh I just googled "Barclays Clydesdale" and it came back with shedloads of results. Martin Lewis does go to great pains to make sure you avoid the pitfall of banking with the same group.
(WillI'mNot logs in twice a year, every year, Sun 19 Jul 2009, 1:26, closed)