bojo as I understand it your DD is doing a Masters, on my recent London Masters too, most students were living at home. Most were funding it themselves, no loans, no bursaries, so it was a means to an end and they had had a taste of independence anyway.
At undergraduate level that is not so true, since most undergrads want a taste of independence. A lot of undergrads are from the greater London area because they realise that they still want the big city, and would find it limited and a bit homogenous elsewhere, but most still want independence. I knew of none living at home on the undergrad level of my course at another London uni you mention nor did my DD's and her peers at UCL. Of course as at any uni there will be undergrads who do chose a local university because for various reasons they want to be at home, and that may mean they are not predisposed, let alone facilitated to mix much socially but I am sure all our universities are large enough for there to be plenty of students who do. I was shocked when I saw the leavers destinations for my old selective school far away from London that so many were going to the local not especially highly ranked uni.
The diversity I referred to was the student body as a whole though, and not just the London area students. A lot of private school pupils do prefer the traditional enclaves like Bristol and Nottingham, to name the universities most popular at my DDs' private school , so the student body tends to be more of a mixed crowd who are seeking something different, from all sorts of different backgrounds.
There are more overseas students, London is their main aspiration but at around 30% at UCL they are certainly not in the majority and my DD appreciated the cultural diversity she was able to experience. A lot of the top unis have a high proportion of overseas students, 22% at Manchester, 25% at Warwick, 22% at Bath but it rarely gets mentioned in reviews of those unversities 
Socially my DD and her peers partied far and wide, the east end is the current focus of most student social lives though they went south of the river too. They also partied with students from the other London unis, despite the obvious rivalries, networks do build up. The night bus network is extensive and these days a shared uber can actually work out cheaper. Actually in the holidays even being here on the outskirts of London is no barrier to going up to and home from town and even the Royal Holloway students out in the wilds of Egham join in getting home on the first train.