I would counter argue that Universities offer very different student experiences, and that it is a reasonable for a 17 year old to be able to work out what might suit them most.
I understand that one of Tizerfizz' DDs went to a non-RG University in London, did not enjoy the experience and does not expect to ever earn enough to repay her student Loan.
This is very different for the experience of my focussed DS who knew absolutely what he wanted to do with his life and why he wanted to take the degree he did. London suited him fine as he was surrounded by equally focussed peers who worked hard, and many of whom, like him did not drink and were not into clubbing. And who, without exception, landed good jobs or went onto further study. They tended to be frugal and use student societies to socialise rather than spend money in pubs and clubs.
It is very MN for people to assume that students are at University for the "experience"" and need funds to hang out in coffee shops, buy nice clothes and toiletries, and to have the money to spend lots on nights out. Doubtless some London students do, but for many it is very possible to live frugally, avoid a party life style, work hard and still have lots of friends and a good time.
Law courses at a number of RG London Universities are well regarded. One tip, used by a friend of DS for banking , but equally applicable to law, is to wander into a city temp agency and say you are looking for a summer job, perhaps as a receptionist or similar, and would prefer something within the legal sector. It won't be a glossy intern gig, but it will be experience and actually other staff are more likely to be helpful and supportive. (Partly my experience as I used to work as a receptionist/switchboard during holidays when at the LSE and learnt a lot about different sorts of organisations working for venture capitalists, law firms and the like.) For a future lawyer the ability to go into law courts, volunteer at legal advice centres and go to lectures given by all sorts of people, and be taught by people who have fingers in various legal pies, etc, should not be underestimated. Yes this will happen elsewhere, but London has more.
OP your daughter sounds great, but then so do you.