As an update, I went in to speak to one of the managers at my branch yesterday. She was very helpful and understanding, which is how it should have been from the start. We established that there were two pages that her colleague had not photocopied from the LPA and these were what Head Office were questioning.
She agreed that the process was poor and that they had let me down, will try to get it sorted on my behalf, compensated me for the cost of travelling into town again and acknowledged my reasons for closing my current account. If her colleagues had been as professional I would not be pulling my hair out or changing the bank I've used all my adult life.
Also, I went into the Post Office who were utterly unhelpful, gave me the wrong forms for my mum's savings account, told me to ring a phone number because they didn't know what they were doing, told me they could not ring the number for me whilst I was at the branch, that I'd have to do it myself. When I did ring, I had been given the wrong number, and the right number was a 15 minute wait to tell me that I will have to send the certified LPA to them. And they won't send it back by Special Delivery like other organisations have said they would try to do.