Is the LPA registered?
An LPA has to be registered to come into effect. This can be done either immediately following it's creation, or later. Some LPAs say they can only be registered when the person creating them (called the donor) loses the capacity to manage their own affairs.
If it is registered, then the Office of the Public Guardian shold have issued you with a certificate - this is legal proof of your being attorney. (By the way, if any financial institution wants to see an original document, never send it away in the post; if necessary, get a certified copy and send that. It's Ok to take an original as proof in person thouogh)
Assuming that the LPA is the financial one and it doesn't place any limitations on what you can do, then you have the legal authority to do pretty much anything your dad could do himself.
For managing a bank or Post Office account (into which a pension is paid), then it should be enough to present your certificate proving you are the attorney and the usual identification. Your authority is legally binding, so a bank (etc) must accept it.
It may be that whoever you saw was simply not familiar with powers of attorney. In that case, ask to speak to someone at managerial level (usually, the larger the branch, the better)
If the LPA is not registered then you will need to do this. The website for the Offic eof the Public Guardian explains how.
There may be some formalities at the Post Office before you can actually draw money. All financial institutions are extremely reluctant to let anyone (even attorneys) use someone else's card, so they might have to issue a separate one for you to use.