London has long featured extremely high housing prices and has been ranked with New York City and San Fran and Los Angeles and Paris as one of the world's most desirable cities.  Post-Brexit, will London lose this elite status?  This raises the issue of what productive and amenity attributes of London will now change?

Will superstars like Elton John continue to want to live there?
Will leading finance firms continue to want to do business there?
Will Europe's talented young people continue to migrate there to work?
Will rich people from Russia and the Middle East continue to park their money there invested in real estate?

A sketch of some answers;

London is unique in terms of temperate climate and beautiful architecture and an orderly European feel while the language is English.  This gives the city a niche such that its dominance will continue. It features street safety and low pollution relative to Europe's other cities. It is classy and historic and this is hard to reproduce elsewhere.

Consumer products in general equilibrium.  Suppose that the EU now slaps 20% tariffs on its products sold in London (think of cheese and wine), given a reasonable price elasticity of demand (perhaps -.4) for such goods, then those who live in London will now pay 8% more for such goods.   That doesn't strike me as a death blow for London.

Worker migration flows.    Now suppose that people born in Germany who seek to work in London must now acquire a work visa.  The British firms will work the hardest to acquire these visas for the most talented Germans.  To be clear, suppose a visa costs $100,000 to obtain.   A British firm who can sign a 5 year contract with a worker would need to prefer the German worker over the British alternative employee by a $20,000 per year productivity differential to justify this visa expenditure.   Note that the most talented Germans would still be employed in London.   In fact, the average quality of German workers in London will increase because of the work visa requirement.

The future of London as a center of finance?  This is a trickier one.   I believe that Wall Street continues to be a center of Finance because Manhattan is such a desirable place to live and work.  The attacks of 9/11 didn't significantly diminish Wall Street. I don't believe that the Brexit matches the shock of 9/11.   Now, the wild card to me is China. If Asia's wealth makes the center of finance move to  Shanghai --- how will London keep its edge as a Center of Finance? Or will Brexit strengthen London as Europe's rich seek a safe haven for where to park their assets as the Euro and Europe face new challenges?

I believe that Manhattan would be a superstar city even if the finance sector was diminished.  There is enough international capital flows and interest in living there that the city would continue to thrive.  My guess is that London falls into the same category.