Someone on AB asked how to prove they had never been divorced and it is of course almost impossible to prove a negative, I imagine the DWP have informed you that they will wish to pay you by direct payment into your bank account and you wish to prove you do not have one, you will have great difficulty doing so.
The government has said that benefit recipients will at the appropriate time, be given information setting out the various account options. If you experience difficulty obtaining your money due to these arrangements, complain to the DWP and/or your MP. The DWP will usually recognise that some people have difficulty, for various reasons, in being paid by direct payment and will pay you by cheque which can be cashed at the Post Office, but take ID.