the most important airport in the world and in critical need of runway capacity, can't get one.
The most important airport in the world at the present time is Hartsfield Atlanta International [101 million pax in 2015] which has five parallel runways in a great layout. Probably sufficient for its needs. If you mean Beijing Capital Airport [90 million pax in 2015] which is catching up rapidly, it has three parallel runways. It probably won't require more, as a new airport for Beijing is under construction at Da Xing. However, it is likely that the Chinese would construct an additional runway if it was deemed necessary. Costs appear to be under control there.
Meanwhile, I cannot think of any UK airport which has been
given a new runway in recent times. They usually cost alot of money. That's the problem.