Every bank should offer a basic banking account. What you get varies on your circumstances, most will not allow a cheque book or debit card but some will allow a switch type account.
Co-op and Barclays are suppose to be the easiest of the banks to get an account with.
Hi, I just came out a Trust Deed last year and managed to get a basic cashline account with RBS. In the last year I have also been accepted for a current account with Smile - the online bank owned by Co-op. You get a visa debit card with this.