This happens primarily because the city of London has a lot of exceptions provided to it by the EU and becomes an attractive place for the Americans, Chinese and Japanese institutions to funnel money into EU markets. It is really in a role similar Hong Kong vis a vis China. With Brexit, EU every reason to promote places like Luxembourg and other financial centers as the financial hub and end exceptions that make City of London competitive. Banks being banks will simply close offices and move business across the water.
Multiple banking houses have at least indicated that they're willing to migrate. Even more important, a lot of financial products in the banking/insurance sector rely on passporting, that is if they're accepted in one EU country, they can be sold anywhere in the EU. That country used to be England up to now. Given that nobody knows if/when the real separation will happen, I fully expect banks and insurances to hedge their bets and start moving that to other countries.
No, it's not evidence since evidence can only be gathered post-fact. Just don't be surprised if they follow through, because well, they told you before which consequences the change would have.
Well so is the parent comment which is arguing essentially that things are fine today and so they will continue be fine in the future.
I'm simply suggesting that may not be the case since EU is now likely incentivized to disrupt the current status if only to set an example. Rather than disrupt physical trade that is linked to export oriented mainland jobs, financial sector may be a riper target as barriers to moving these jobs are low (essentially no capital investment), disrupting it can be used to create jobs on the mainland and can create a punitive effect on UK.
London is very expensive. Banks already have significant motivation to move operations somewhere cheaper, and have been doing so when they can.
That said, whilst it may seem tempting to run to the EU, other countries have been wanting to kill off the city and take its profits for their own for a long time. In the event of a remain vote, they may simply have been emboldened to outvote the UK and do it anyway, hence the focus in Cameron's negotiations on protecting the City. He knows it is vulnerable.
The banks now face a choice. Which is more risky/expensive. Needing to go through separate EU regulatory processes and get an EU "passport" via a subsidiary. Or relocate to e.g. Paris, and have all their activity be regulated by an EU now dominated by socialist governments rather than just some of it.