This in large part, would be down to the City of London, now the Corporation of London and the geographical area[s] that it governs. /u/feezec is correct to point you towards CGPGrey's video about London, and how not to confuse the City of London with Westminster and Greater London (If you did not already know the difference).

From the history section of the Corporation's website;

"The right of the City to run its own affairs was gradually won as concessions were gained from the Crown. London's importance as a centre of trade, population and wealth secured it rights and liberties earlier than other towns and cities. From medieval to Stuart times the City was the major source of financial loans to monarchs, who sought funds to support their policies at home and abroad. In early times London was two cities – the trading and residential City of London (around St Paul’s) and the royal, administrative and religious West-minster. As London grew, the City specialised in trade."

This relative autonomy of the City, the wealth it accumulated through trade and taxation almost independent of the Crown, and the influence it gained from outside the city walls allowed it to flourish over the centuries and continue to gain special dispensations.

As the centuries passed, the City of London, Westminster and many of the towns and villages outside of the walls and administrative districts formed a conurbation that we now define as Greater London.

A good book that Chronicles London's success (and indeed failures) is London a History by Jeremy Black . Another interesting book, if you like your historical maps like I do, is London a History in Maps by Peter Barber, which really puts the development of the city into a visual perspective.