loofah, I assume your DD might be in a position that many Londoners find themselves in. UCL, LSE, Imperial, KCL etc offer some very good, internationally recognised, courses, which can be the best academic option, especially for those rejected by Oxbridge. So the obvious choice even if you don't want to stay in your home town.
It worked out well for DS, who stayed on at LSE for his Masters even though he had an offer from Oxford, and indeed for some of his friends who thrived at UCL and Imperial, and who gained great starts to their future careers.
London Universities are different from Oxbridge, which is again different from campus universities or from places like Bristol. It is hard to generalise but I think engagement is the key. Engage with your fellow students, wherever they come from and whatever background they have, and it will be an enriching experience. Engage with the academic side, including joining the subject society and attending office hours. Just about everyone passes through London so there is huge scope for enrichment activities such as talks by visiting lecturers. A personal view, though I may get flamed, is that some students stick within narrow social groups and spend time in the library rather than showing an interest in broader aspects of their subject. (The LSE cliché is the student determined to get their first and their job with Goldman Sachs, with the degree just a means to an end.) DS found that most academics were therefore really supportive to undergraduates who showed active interest in what they were being taught.
Then be proactive with a social life. Join things. It is not quite as easy as Universities where you can normally count on making friends in your flat or in your hall. People are scattered, but there are plenty of societies, sports and so on, and a chance to make friends with people who share your interests.
The transition can be easier. In his first term DS saw old school friends who were at UCL and Imperial, as well as one who was taking a gap year. And those at Oxbridge initially seemed to be returning every other weekend. (DD found plenty in Bristol who went home most weekends in their first term.) Slowly the balance shifted as he and others got caught up in University life. Studying in London is quite different from either being a child in London or working there, and it often requires a level of self-motivation. But if you have that, it can be really rewarding.