If you have a higher income than the OP and want to live in London, you can. But you might have a lot less money to spend on things other than housing which might not be to your taste. I have a lower income than the OP and live in London. There are absolutely tons of people on low incomes who live in London.
If you want a 700K house in London, then you might be able to do that if you want to as you are on a higher income than the OP, especially if you have good prospects and a decent deposit (you probably do if you already have a house of whatever value or size). Maybe you don't want that. That's fine! It's not compulsory.
The OP has no way of funding full school fees and her children will be competing against everyone who wants to apply for the school, no matter what their income. Bursaries for children who pass the exam will be awarded on need as well as performance in the exam. If a child whose parents earn £25K each does a lot better, maybe they will get a bursary and the OP will be lower down the list. Maybe there are a lot of bursaries available but people aren't choosing to apply for them where they might and prefer a grammar or a good comprehensive if they are lucky enough to live near one. Maybe you don't really know how this actually works or what the OP has chosen to put her money into. For all you know she's inherited the actual house and just decided to live in it rather than selling it.
I don't think OP is likely to get a 100% bursary but she might given what she has said about spending £50 a week on food which is extremely low as a weekly food budget by anyone's standards. Who knows.
Ultimately schools give bursaries to children they think would benefit from attending the school and who cannot otherwise pay the fees and it is their decision. There is a cut off but this is obviously higher in London as there are higher living costs. Nobody is stopping children from much lower income families applying, or indeed children from higher income families applying. The cut off for a bursary at some London schools is around £120K because these people would otherwise be unable to afford to spend £30K per year per child on school fees. And it might be higher if they have more than one dependent child.
You might think that bursaries should only be for children from families on very low incomes, but the school just want the children who will benefit most from the education offered. Some schools in London are really very selective. They will just choose the most intelligent children that they can, regardless of income.
Sorry, v long.