Morrisons: well what this "should" mean is that the EPA has been registered with the COP and has been shown to be valid. In fact, if it hasn't been registered it "technically" isn't an EPA - it's an instrument to create an EPA.
Having said that, I assume you also saw this
http://www.halifax.co.uk/HelpCentre/poa.asp
"As an appointed representative, you may be able to manage your appointed accounts online (excludes Court of Protection registered customers or those acting on their behalf)."
I have to say, on that basis, I and JPG1's "Dave" was incorrect (at least as far as Halifax's stated policies) - if you are using any form of registered EPA/LPA online banking is not an option at Halifax.
Their PDf brochure also says (in teeny, tiny letters) at the bottom of Page 7.
†The Online Banking service is not available for Court of Protection registered customers or those acting on their behalf e.g. a loss of mental capacity.
My feeling is that you can continue to try and fight this or you can do what other people do - find a bank who are happy to have your custom. I feel Halifax are incorrect, but being a carer is hard enough without this sort of thing.
P.S. Cross Posted with Nitram: exactly