Brexit has already been disastrous for The City, and it looks to become more so. It's practically the only thing that could unseat London as the premiere european finacial hub. Brexit is everything The City dreaded.
> They are by far the largest and most influential entity and one of the only few that are going to be better off after Brexit.
That is now what outside experts predict, nor is what the banks themselves are predicting, nor is it in line with how they are acting, nor is it matched by what has already taken place.
> staying in the EU would actually jeopardize their special tax-heaven status as EU was moving toward more banking regulation
First, I don't think you 100% understand what regulations are at issue here; there is no "special tax-heaven[sic] status".
But yes, there are rules changes coming that are designed to hamper The City and (not at all coincidentalyl) to push banks from London to Frankfurt. And inside the EU, the UK had some ability to lobby for tweaks to weaken or avoid these regulations. Outside they do not. This isn't a way for them to avoid this issue, this is a way to ensure that can't. For the bankers, Brexit is seen as an existential threat. Just look through the Brexit related headlines on, eg, Bloomberg. It's unmitigated doom, gloom, and panic.
From https://www.bloomberg.com/graphics/2017-brexit-bankers/:
> Frankfurt has emerged as the biggest winner in the fight for thousands of London-based jobs that will have to be relocated to new hubs inside the European Union after Brexit.
> Morgan Stanley, Citigroup Inc., Standard Chartered Plc and Nomura Holdings Inc have picked the German city for their EU headquarters to ensure continued access to the single market. Goldman Sachs Group Inc. and UBS Group AG are weighing a similar decision, said people familiar with the matter, asking not to be named because the plans aren’t public. HSBC Holdings Plc is the biggest non-French bank so far to opt for Paris, while Barclays Bank Plc has plumped for Dublin.
> London could lose 10,000 banking jobs and 20,000 roles in financial services as clients move 1.8 trillion euros ($2.1 trillion) of assets out of the U.K. on Brexit, according to think-tank Bruegel. The implications for the U.K. are substantial: finance and related professional services bring in some £190 billion ($248 billion) a year, representing 12 percent of the British economy.
Brexit is already gutting the UK financial sector, full stop.