Your best bet is your bank. A lot of funders are careful about lending to people on benefits as if you were to not pay them it is difficult to get a court to grant a payment order for anything more than a few pounds per month.
Having said that if your benefits have been going into a bank, the bank will probably see you as okay
Just go for it, I would. Try filling in a loan application online just to see if they approve you. If they don't, then you already know the answer. If they do, then hurrah!
I'd agree with scarlett and say use an online application. Besides not having the potential embarassment of the bank turning you down, the rates are likely to be way lower than a bank. Banks charge a fortune compared to something like Northern Rock or Cahoot online.