Well your bank account doesn't have to be moved if UK is still the best place for all your banking needs. It would be a potential loss of business for UK's financial sector but also might be a reduction of your banking welfare. It's a lose-lose situation for everybody but it doesn't have to be this way if EU can just set aside its personal vendetta to negotiate reasonable and mutually beneficial agreements with UK to adjust for UK's changed membership status with EU. Right now the problem is EU is not negotiating in good faith with UK to arrive at a mutually beneficial agreement for both EU and UK but instead is choosing to take a condescending and vindictive approach to make Britain's transition to be outside of EU as punishing to Britain as possible. Well that's not going to work well for UK, EU or the world even.
It's not really in EU's interest to negotiate in good faith. The amount of resources going into this Brexit is immense and obviously the EU wants it to be as hard as possible to set an example. It was never meant to be an union from which you can pop in and out.
Regarding banking, there are EU regulations and UK outside of EU is just another territory, unlike now. Regarding the funds safety, for most people Germany or Sweden is as good as the UK, it's not really a big loss for them.