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?
Remove that possibility, then people will consider other places as well.
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 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.
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.