You are legally entitled to a basic bank account. You are not required to provide utility bills or have a fixed address. The law changed in September 2016, so some banks may not be aware of it and some may not be keen to provide a basic bank account because it may be expensive for them.
If you have difficulties opening up a bank account, you can let your chosen bank know that the law on basic bank accounts changed in September 2016. This means that banks now have to offer basic bank accounts (ones with no overdraft facilities) to anyone legally residing in the EU. The only exception is people who have criminal convictions for fraud. The new laws took effect on 18th September 2016 and are set out in the EU Payment Accounts Directive.
You can use this Letter as a template, which has all of the information you need.
If you have any issues opening a bank account, please contact the Friends, Families and Travellers national helpline on 01273 234 777 and we will be happy to help out.