Not that many tall buildings, no, especially relative to the size of the city like you say. But now there are quite a lot more on the way.

See: http://farm6.static.flickr.com/5092/5572644244_632616f87c_b.jpg

All buildings with white text are already built (complete) the ones with yellow text are currently under construction and with red text are approved and awaiting construction.

Most of the buildings I did for 2027 will in fact be built before this decade ends say 2019.

The leftmost one in the 1997/2007 charts is 1 Canada Sq, ie the tallest building in this submission photo and tallest (finished) building in London/UK overall. Which, as it happens, is exactly 50 floors, so if that's your cut-off point for "taller buildings", we have a grand total of... one. (Or 2, including the unfinished Shard).

Even with all those new ones built, we'll still be a long way from rivalling the skyline of NY, Chicago or HK for scale, particularly as they are mostly growing up in separate clusters (Canary Wharf, the City, LBQ, Vauxhall) rather than a solid spread. But it's an improvement on our completely embarrassing paucity at least. And I'm pleased that the powers that be seem to be thinking "quality over quantity". Gherkin seemed to set the trend and the Shard, Strata, Pinnacle ("Helter Skelter"), Leadenhall st ("Cheesegrater"), etc seem to confirm it: most of the big future projects are at least somewhat architecturally 'interesting' designs. Some of them divide opinion, to put it politely (I fucking hate the walkie talkie, for example) but that's better than all identikit plain cuboids, I think.

tl;dr - London's never going to be remotely a contender for highest or densest skyline, but we seem to be having a stab at being one of the more interesting.

For more detail on all the future projects (and credit as to where I got that diagram from): http://www.skyscrapercity.com/showthread.php?t=977690 - (diagram came from page 17)