I think you may have misunderstood the problem. It's not that we don't know how to build dense modern cities (just look at China). It's that London has made a

I think you may have misunderstood the problem. It's not that we don't know how to build dense modern cities (just look at China). It's that London has made a very concerted effort not to be dense or modern. There are (finally) skyscrapers being built in London, but even now they are limited to a few specific areas. Views of St Paul's and Westminster are especially protected. Which is fine, and understandable! But you're asking, I think, "why doesn't London become a bit more like Beijing or Tokyo", and the answer is "because London really doesn't want to become like them". Building a bunch of small apartments would absolutely solve the issue (and cause others; a lot of London infrastructure is close to capacity), but it's a solution which is politically impossible. Interesting article on the subject here: http://www.economist.com/news/britain/21596539-capitals-skyline-growing-mess-let-boris-sort-it-out-ascent-city http://www.economist.com/news/britain/21596539-capitals-skyl...