Proving the identity of someone under Power of Attorney

I've had two situations recently where I've been asked to provide proof of address for my mother when acting under Lasting Power of Attorney.  This is getting increasingly difficult as my mother has lived in a care home for the last five years and has no current passport, driving licence or utility bills.

One company accepted a letter from the carehome and the other wouldn't.

The British Banking Association have published a useful leaflet here

http://www.bba.org.uk/publications/entry/guidance-for-people-wanting-to-manage-a-bank-account-for-someone-else/leaflets/

But the answer to the question of how to prove identity in this situation is still unclear - it says that a letter from an appropriate person may provide the necessary evidence but it's not clear who decides whether it does or not.