Proof of address is one of the requirements to open a UK bank account.  The rules are laid down by the [Joint Money Laundering Steering Group][1], which reports to the [Financial Conduct Authority][2] (FCA), which in turn reports to the [Home Office][3]. The FCA regulates both wholesale and retail banking.

Invariably, this requirement causes the most frustration for newly arrived immigrants, and admittedly the conditions are fuzzy. Generally, documents meeting this requirement will show the following characteristics:

 - The document is system generated, although tenancy agreements and/or
   correspondence from a solicitor can also be accepted; also
   correspondence from an agency in the UK government, such as HMRC can
   be accepted;
 - The document has a date and is current, usually issued in the last 6
   months, but shorter periods may apply in some cases, a TV license for
   example;
 - The document shows the same name and address as given on the bank
   account application;
 - The document is from an acceptable source and clearly shows that the
   person has an account or customer identification registered in their
   name;
 - The document is not a bill for a mobile telephone; and
 - It is not the same document presented as proof of identity.

There is no discretion on the proof of address requirement. Some banks may want to see heating and electricity bills to see if consumption is in line with a resident. There's more info in an article I wrote on the topic which is here http://www.londonelegance.com/transpondia/other/forms-of-identification

Note that they are rolling out the new landlord requirements for immigrants seeking tenancy agreements, so this may make getting a tenancy agreement more difficult. 

  [1]: http://www.jmlsg.org.uk/bba/jsp/polopoly.jsp?d=749
  [2]: http://www.fca.org.uk/
  [3]: https://www.gov.uk/government/organisations/home-office