Its actually because they used to be so crap!
20 years ago all of the London Boroughs/Local Education Authorities were at the bottom of the league table. I lived in Hackney, it was third from the bottom.
Then finally, just over ten years ago, the government forcefully took over a number of London education authorities, either by failing them or just by taking over completely. Hackney had some kind of special NGO set up to deal with the mess that was state education in Hackney (particuarly secondary, primary seemed to be pretty good weirdly).
It was talked about v little. Firstly because the chattering classes had sent their children to schools crapper than they would like to admit and secondly because its rare for London to be looked at negatively in the media, in some ways.
Then all of the pilots for things like free schools and academies got centred on those failing areas in London, which meant they had a huge amount of money coming into them. This improved them at a faster rate than the rest of the country.
I also think teaching has always been very good in London. I moved out of London at 16 and was shocked at the general don't care attitude of many teachers across the board. Teachers outside of London were lazy in a way that would have been unthinkable in any of the secondary schools I experienced/friends and family experienced. As I said, I was shocked by that when I moved!
Not sure why. Maybe teachers in London are more idealistic and move their for a challenge? But it can't be that simple can it?