Have you tried asking her what she think's she'll need to spend money on, and how much that'll be? From what you've said about her, she actually sounds reasonably sensible (but maybe a little spoiled).
I'd say the £500 she's got left per month will be enough for her to feed herself, socialise, and treat herself occasionally.
You probably want to focus on setting her up well, then you can evaluate where she's at after the first chunk of uni (eg at reading week or xmas).
Get her to make a list of what she'll need before she goes to uni, and perhaps give her a budget for that, and take her shopping. (eg bedding, room accessories, crockery, cookware, some new clothes, a couple of decent pairs of shoes for walking everywhere, a warm and waterproof coat, a laptop, new stationary, a decent backpack, extension leads, maybe a set of plastic drawers, and any sports gear she doesn't have already).
Take her to do a big supermarket shop when you first drop her off, get a big bag of dried pasta, tins of soup, tins of tomatoes, big bag of rice, big pack of laundry detergent, the usual weekly shop bits, some chocolate, biscuits etc as nice treats and a big bottle of her favourite spirit.
Leave her with some money to cover any course books she needs (most will be freely available in the library), registration fees for the student union, any societies she wants to join, and her sports team fees.
Then say "see you when you come home for reading week. Let us know if you're really struggling for food and we'll do you an online shop."
Then once she's home, you can check in with how she is for money, if she's struggled, go through her bank statements together and see what she can cut out, or where she might genuinely need a hand.
Then do the same when she comes home for xmas, and easter, and summer.
If she's managed fine, you can then move some of the money you thought you'd be giving her into a savings account in her name, that she can have when she graduates. If she's not, then you can go through with her and create a budget, look at giving her an allowance, and her getting a job through the summer or part time if she hasn't already.