Yes, I often asked myself the same question. But actually billionaires don't live in London much, they purchase houses, which is very different. They believe, or are made to believe that it is a safe investment. They, together with a large number of top bankers and young wealthy people from all over the world have led to this huge housing bubble in the last 25 years. Also, New York's economic/political fall in 2001 has contributed. London is indeed a horrible city and houses are, per se, worthless. High price have been made possible by its strategic financial, historical and political situation in the Western World. During financial crises, London house prices have suffered more than anywhere else. Not saying that house prices will fall dramatically as a result of this crisis and even if they did, it would be a slow decline, as alternatives are not easy.
Tax reasons - they don't pay tax. London is a great place for corrupt business men and politicians to hide their money. Most only stay a few months though so don't think they come here for the dreary weather. You'd find that their properties are empty for 90% if the time.