Tiger, which is your DC at, as I am not sure I recognise your problem. If you don’t have a DC there, I think you need to be careful about repeating old saws as if they were truths. You regularly post quite negatively about London. Fine if it is genuine experience, but otherwise it’s odd. From what I recall your DD2 studied fashion in London at a non RG, about a decade ago and lived way out and was quite unhappy. But that experience does not necessarily predict the experience of someone starting UCL now. I also fail to underwhy your DD1 would see international students on an MFL course as a negative. Does MFL suggest an interest in communicating with non English speaking people. FWIW, both my DC considered the diversity of London universities as one of the strengths, not least a good preparation for an international career.
DS was at LSE but 3 or so years ago. Guaranteed first year in halls, which may be intercollegiate ones, but none too far away. It used to be that UCL also guaranteed places, but Kings did not, so worth checking.
DS then shared an ex council flat near Great Ormond Street. Quite cramped as they used the living room as a bedroom but really central. No more expensive than, say, Bristol. The good thing about London, or at least LSE is that the campus/SU/library is open late so tends to be the social focus point.
I also went to LSE and we were determined to look down on Strand Poly (KCL) However it is fine and has some strong departments. Do look at War Studies. LSE seems to be able to find numbers in anything, so check course content if you don’t like maths. UCL has the advantage of a wider range of subjects, even more if you add the Slade and Rada. It also offers a terrific range of years abroad, and it’s Liberal Arts degrees are worth a look if your DC is undecided.