£250 per week nett for a live in job is perfectly legal and, in my opinion, is not a pittance. I don't have £1000 a month for disposable income after paying taxes, buy groceries, paying rent, paying the nanny, etc.
As for children cooking for themselves... well, quite frankly, I think it is a good thing. Perhaps the ingredients should monitored omore closely (like make sure some veg gets under the cheese on the pizza). My 4 year old can make pizza and I encourage this. But I do have coax her into adding spinach.
I agree with nannynick that it doesn't sound like you followed normal disciplinary procedures. My nanny would have to have done something far more serious than letting the children cook for themselves to be fired on the spot. If I walked in and found her snorting cocaine with kids, or I came home and found she wasn't even there, then I'd send her packing on the spot. I think you have gotten a rough ride on this thread (and I'm impressed with how calm you have been in response), but I'm sorry to say I do think you overreacted in firing her. What I probably would have done is asked her to implement a nanny diary / meal planner the week before so you can buy the proper ingredients at the store.
Now, are her duties a resonable expectation? I think they are, actually. Several people have mention her long 24 hour day. But considering that none of your children are toddler/babies I don't think that is that much work, especially if someone else is educating them and she is supervising homework like any other nanny would likely do after the kids got home for school. Anything that relates to the welfare, education, care of the children is pretty much fair game for nanny duties.
Let's see. What are your options now? You mentioned reducing your hours. But do you really want to do this and is it really an option if you run your own business? You could perhaps hire a live-in nanny and an au pair. The au pair could pick up the less interesting work like laundry, cleaning, she could run to the store when your nanny needs to stay home with the SN child. And she could generally be an extra pair of hands. She would work about 25 hours per week so possibly just mornings or just afternoons. And it would cost you oh I don't know maybe £60 per week, tax free.