Honestly, you should be really proud of yourself. LSE, for some courses, can be just as hard to get into as Oxbridge. You're going to be studying Economics at London School of Economics, clearly you're in good hands.
It's perfectly understandable that you'd be upset over Cambridge (it probably stings even worse because some of your friends have been accepted), but try not to be too concerned about them. You're running your own race. And if you get a 2:1 or 1st class degree, the world will be your oyster.