We have Canary Wharf, but that’s tiny compared to some of the beasts in the USA. London is a major financial centre and a large city, so why hardly any skyscrapers?
This article, although it is from a fairly biased (anti-skyscraper) source, mentions a couple of the reasons:
Proximity of flight paths - buildings over 1000ft are banned in Central London.
Protected views - buildings are not allowed to block certain lines of sight of historic monuments, e.g St Paul’s Cathedral.
Pretty much the same reason DC lacks them - London officials wanted to protect the view of the traditional skyline including Westminster Abbey, the Parliament clocktower and St. Paul’s. There used to be an upper limit of 400 ft., and even this was controversial.
They’re also reluctant to build them around St. James Park and the area because you could look into the gardens of Buckingham Palace and it would be a security hassle.
It’s also partly for the same reason that LA doesn’t have a lot of massive buildings. It’s a lot cheaper to expand horizontally than to expand vertically. New York didn’t have the option since they ran out of space on the island and were forced to grow vertically, resulting in the famous skyline.
Another factor not mentioned there, but which I imagine has an impact on planning decisions, is the fact the central London still largely has its medieval street pattern of narrow winding lanes and alleys, not the wide straight streets of most American cities. Fitting skyscrapers in between these lanes would cause unacceptable overshadowing - imagine “canyons” as deep as those in Manhattan, but with a street only 20 or 30 feet wide at the bottom.
Another reason is simply there isn’t a commercial rationale - even the Gherkin has empty space - never mind some of the other office buildings. Rents don’t make it worthwhile (and you’d have serious trouble trying to sell space in a really big NYC type sky scraper - it’s too obvious a target)
Maybe London doesn’t have WTC-style towers but have you looked at the Docklands lately? Tall buildings are sprouting like weeds. And then there’s the f***ing Gherkin (which, if you haven’t guessed, I hate).
London is moving up.
The Gherkin’s the one that looks like a large penis covered in scaffolding, right? That’s definitely an unfortunate addition to the skyline.
Should you wish to, you can see into the Queen’s back garden from the (horrible) Hilton in Park lane - they even have a cocktail bar (full of complete and utter cocks) to allow you to do it.
That’s the one. Also known as the Swiss Re Tower, or 30 St Mary Axe.
I quite like it (It’s given name is 40 St Mary Axe, which I have never heard anyone use). I prefer it to Canary Wharf (which looks like it’s made of lego)
Without getting into IMHO territory too much, I like that building. Better that than anotherCentre Point or New Zealand House, say (Note to Kiwis: you have one of the most beautiful countries in the world, so why in God’s name did you visit this monstrosity on central London?).
The only bad thing about the “Gherkin” is that, because of its shape, on a sunny day one of its panels will always be directing the sun straight into your eyes 
Might it also be something to do with London’s geology, perhaps? London Clay may not provide the best of foundations for such heavy weights.
I believe geology also explains why in Manhattan there are very tall buildings at the southern tip (er, two fewer these days) but then a gap before they begin again in earnest round about the Empire State building.
Although, as Colophon says, this article is fairly biased, it does pinpoint some of the political tensions involved.
The Corporation of London (which governs the Square Mile) has long favoured creating as much office space as possible (i.e. build more skyscrappers) and, more recently, the Mayor of London, Ken Livingstone, has adopted the same view. However, tall buildings in the City require planning permission from central government, in the form of the Secretary of State for the Environment, and Whitehall has usually been much more sceptical. Any pressure from the Corporation of London for skyscrappers is usually counterbalanced by pressure against from English Heritage. The protected views of St. Paul’s and the Palace of Westminster are the extreme example of central government imposing planning policy from above, as those were legislated for by Parliament, not by the local authorities.
This site claims that the geology is similar to Chicago, so that doesn’t explain it (no idea how reliable a cite that is, though 
)
It’s south of the Thames that you run into trouble with much softer ground - so soft that tunnelling is difficult, which is why the Underground mainly remained to the north of the river with overland rail dominating southern routes.
I’ll never forgive Philadelphia for dropping the “no building taller than City Hall” rule and putting up a bunch of crappy skyscrapers, ruining the skyline.
They waited till I left, as they knew I would never have put up with that. “OK, she’s moved to Baltimore—start your engines!”
Manhattan is pretty much all solid rock. The reason for skyscrapers at the southern end is because New York started there and grew northward, so it has always been the commercial center of the area. The reason you also find them in midtown is proximity to them newfangled railroad stations. (Penn at 34th St., and Grand Central Terminal at 42nd Street.) Also the subways helped move business north.
If you want to see a NYC building that really sticks out like a sore thumb, though, check out the Citibank tower in Long Island City.
That’s not what I’ve read in several places. For example, in Annals of the the Former World, John McPhee talks about the presence of bedrock near the surface in Manhattan:
It’s cheaper in the short run to expand horizontally, but in the long run it’s more expensive in terms of fuel consumption, traffic, and commuting time.
I looked at that on the web. It is a strange looking building isn’t it.
Here are some pictures the building. Most developers try and stay away from round buildings.