OP I am
at some of the responses. I spent part of yesterday talking to an old friend, who is equally trying to hold it together financially, so that her kids don't face disruption as she works out how to pay for a good divorce lawyer who will find the money her future exDH is busy hiding.
I wonder whether your post is about something different. You are working yourself to the bone, yet your daughter is splurging on clothes, nights out and make up. You are worrying about whether you can afford to help her. Yet even if you do there is every chance that she will also fritter through her overdraft looking for you to bail her out.
To be honest I dont think she will find it easy to find a grant. Her case does not sound very "worthy".
At some point you are going to have to tell her that the bank of mum is closed for business. I think this might as well be now.
Her choices are either to save every penny from now on. Zero spend on anything not vital, and spend the next two months learning to cook and clean. (She can do both for you.)
Or she takes another gap year , and another even, till she is "ready" to go to University. There are huge temptations for freshers. As you will see from these threads, kids can have quite generous allowances, and quite probably, are also building up overdrafts. However this is not true of all. DD, who likes cooking and sport, but who is not too bothered about drinking and big nights out, spent about £50 a week in the last two weeks, and still has her gap year savings as a buffer. Nothing remarkable about that. She would get less if she were on the dole. (And if she were ever broke, she , like you, would survive.)
You owe yourself a break. Think a bit about why she is not supporting you - presumably it is part of the back story. Then be clear. You have struggled long enough. She is an adult. A second gap year might not be fun, but she has squandered the first, and you have no more to give. At some point in the future, she may tell you you did her a favour. No point in picking the best course in Britain if you are not ready to make the most of it.