Going against the flow, but I don't think £400 is a lot to be honest, when you factor in books for her course, which are often very expensive, travel costs, personal toiletries etc and socialising. I imagine that she is spending a lot of time out and about and meeting new friends, which is what students generally do if they can afford it.
I have two daughters at university and pay them each a monthly allowance of £600, but they have to buy their own food out of that as they are not in 'lodgings'. They both manage fine but they do not live in any way extravagantly, hardly drink etc.
I would be inclined to have a face to face conversation, ask her how she is settling in, what she is doing etc, and she is likely to tell you of any problems, if you have a close relationship, which it sounds as though you do. If you suggest that she is spending too much, she is likely to clam up and feel uncomfortable and potentially guilty when she is spending money on going out or doing normal things that students do. You are giving her a wonderful gift and you say that you can afford it, so let her just enjoy it. If it's her first time away from home it may take her a little while to learn to budget, but she will get there in the end!