Because we value our old buildings AND the London view must be protected. There are also many more rules and regulations and many of these are protected listed buildings (Listed means it cannot be changed without permission and needs to be in keeping with it's current looks)
We do not need 20 towers dominating everything else that is beautiful and lovely about the city skyline, we also have resential areas among the city trading areas as well as parks and tourist attractions and we are much more mixed up than America in terms of lay outs of roads and housing.
I for one pray that London skyline NEVER gets too overcrowded with skyscrapers, there are plenty of decent sized buildings, lovely buildings, interesting buildings and we not need to build more and more towers, higher and higher buildings, just to be ahead of the USA or because you think it *looks* nice.
We have own special mix, just like you do. We need to keep that, not look like every other city in every other country.