Can’t I just get a letter from Mum giving me authority?

It is up to the organization that you have to deal with as to what authority they require. The Land and Property Information Office which controls the ownership of real estate and therefore buying and selling of houses insist on a Registered Power of Attorney. Centrelink seems to have its own form of authority and banks usually insist on a Power of Attorney but not usually a registered one. A bank will usually have a procedure to authorize someone else to sign on an account and this may solve the problem of paying bills.