No, London will still be London. Why do people think that suddenly you might have to apply for a visa people will stop wanting to come and live in London?
Because they don't live in London just because they like Big Ben; they go there for the jobs and the economy. With a hard Brexit, that all disappears because the only reason London is the economic powerhouse that it is is because of its position within the EU. When that disappears, the reason for all the banks to be there will also disappear, and the local economy will collapse. When that happens, people will be moving out in droves.
> With a hard Brexit, that all disappears because the only reason London is the economic powerhouse that it is is because of its position within the EU.
This may be the only reason it has retained the role, but it had the role for a couple centuries before the EU, largely due to its historical position in the Empire and inertia. I don't think the essential connection of the role to the EU is universally accepted. Though we'll certainly see if it's true...
The Empire is long since dead and gone, and small has-been nations with little significant industry cannot retain world-leading status forever on inertia alone. Just look at Italy; where are they now? They make some great olive oil I guess, and a few really nice cars, but they're not the powerhouse they were 2000 years ago.
The essential connection of the role to the EU may not be universally accepted, but it's also not universally accepted that the world is round or that humans visited the Moon. The EU countries are more prosperous economically for the same reason the US has been prosperous for a long time: having tons of different currencies and massive transaction overhead (customs, duties, different regulations to follow, etc.) every time you cross a border is bad for economies. North Korea is a good example of how a country does economically without significant trade.
The French have been claiming the end of the City of London and Anglo-Saxon capitalism since the 16th century. Other than the outbreak of WWI, I can't think of a single example that had a material, long lasting effect on London as a center for global finance.
Yes, London is at an inflection point. Then again, so is the EU, traditional commercial banking and global finance in general. Brexit pales in comparison to these things.
Remove that possibility, then people will consider other places as well.