yes people can take photocopies of official documents without permission. If the hospital has lost your document, I would be asking THEM what THEY are going to do about the loss.
I am assuming as she lacks capacity, you have had to register the documents (old style) or get it officially registered as part of the original process. I would be going back to the Office of the Public Guardian, telling them what has happened and asking them how to proceed.
edit: yup, you go back to the OPG and they provide certified copies for a fee which o would be expecting the hospital to pay.