Sigh the requirement to have a EU subsidiary only concerns conducting active marketing campaigns within the EU or having offices in the EU, nothing is preventing EU customers from seeking to open accounts with foreign banks. UK banks do not need to advertise in the EU. They will not be able to have offices in Eu countries without a license but frankly today you do not need physical office of the bank near you, possible exception is retail banking catering to business with cash transactions.
To word it exactly Banks not licensed in the EU can not offer services in the EU but nothing is stooping them from offering services in the UK to EU residents, with the technological progress there is little disadvantage to this. With a liberal regulation account can be opened from your home over the internet. Do you people really think that all 300 (rough number) Swiss banks do not have significant European clientele? Or that they all have EU passports? Until recently the fact that they did not have a physical presence in the EU was even a major advantage.