Dear Kate,
I only understand what you are going through too well.
My mother just died (24th of Dec). She had Alzheimers as well. The beginning of 2007, we managed to place her in a retirements home, special ward for Alzheimers patients. Of course she refused, but we couldn't cope anymore. She needed full time looking after. And guess what ? She was actually happy that last year. She had people she could talk to and there was entertainment every day. And when we went for a visit she was always happily surprised that we had found her there (she thought she was in the pub).
I don't know how things work in the UK (I am Belgian) but if you can find a decent nursing home for your mum, do it ! When my mother was still at home, she was nasty as well. Once she had been in the retirements home for a while, she actually became pleasent. The people there have such experience, know how to handle them. But you must be sure you find a good place. I've heard other stories.
Yes, you will feel guilty in the beginning, 'locking her away', but you will actually be doing her a favour. That is my personel feeling. She will get proper care, by people who know what to do, and you can visit as often as you like and you will be able to enjoy your mother's company again.
How to get the care people (sorry I don't recognize all your local abbreviations)as far to understand how serious the problem is : I actually wrote down on paper all the little incidents that where an indication of her illness (like she went wandering around the neighbourhood not wearing a coat in the middle of winter etc)and we managed to organize a meeting with us (the children), her local docter and the care people. And then they finally agreed the situation was critical. It wasn't easy to do so, but if you keep bothering them, in the end they will agree on a meeting.
Good luck, and remember, you are not alone