Beyond the fact that most money to be invested in funds is already managed from London, you have the fact that this functions in English, most often using English law, and that the other players are already in London - that's where the game is.
And of course, for such big amounts of money, tax rates are more favorable in London (although it depends on your family situation: with kids, the calculation is not quite the same).
but essentially, private equity is where people hope to cash in on get-rich-quick schemes - this being driven by the asset price bubble (which means that I think today is not a great time to jump in). In the long run, we're all dead. John Maynard Keynes