I wrote this as a response to someone on B3ta, but realised it might be useful for a wider audience:
First, get your debts cancelled, written off, paid, or otherwise disposed of. The Citizens Advice Bureau will explain this best. Don’t pay anyone anything for advice – it won’t be any better than the CAB’s free service.
With your debt cancelled, first get a Basic Bank Account (here) – these are offered by most major banks, even if your credit is unimaginably bad, and mean that you can get paid your salary into your own account and take out cash from machines. It doesn’t give you a debit card or an overdraft. If this goes OK, your bank should be able to upgrade to a debit card account, or at least an Electron/Solo card account, before too long.
In the meantime, if you’re confident you won’t be tempted to spend the money, then also apply for a ‘people with dodgy history’ credit card with someone like Vanquis Bank. This will charge you an eye-raping rate of interest, but the reason you’re getting it isn’t to borrow money: just buy a tenner’s worth of petrol on it once a month and make sure you always pay off the fiver minimum balance, which will demonstrate that you can be trusted with having a credit card and making regular payments (pay off the rest of the balance every three months or so, before it gets out of hand).
Make sure you’re on the electoral register, try and make sure your name’s on the electricity, water, phone bills, and try and get a contract mobile once you’ve had the bank account and the credit card for a few months (even if that means paying them a deposit). That should all help – but in the end it’s a waiting game.
By all means comment on anything I’ve missed or that’s ropey…