That's not actually certain. The UK has no fundamental reason not to recognise EU banking licenses, although it may choose not to, or to recognise it but require additional compliance.
The UK may end up being 'forced' to not recognise such licenses in retaliation if the EU refuses to recognise British licenses. This is quite likely to happen because the EU has a track record of revoking financial licensing as part of trade wars with European countries. For instance they revoked acceptance of Switzerland's financial licenses as part of trying to pressure the Swiss government to cede significant powers to Brussels.
the PRA has stated that EEA firms will require a license (with some temporary transition arrangements:
> Passporting rights will now cease at the end of the transition period. Once passporting rights cease, EEA firms currently operating through a passport in the UK under the existing European passport framework will require a Part 4A permission under the Financial Services and Markets Act (FSMA) to be able to continue carrying out regulated activities in the UK.
> This is quite likely to happen because the EU has a track record of revoking financial licensing as part of trade wars with European countries. For instance they revoked acceptance of Switzerland's financial licenses as part of trying to pressure the Swiss government to cede significant powers to Brussels.
this is the worst example possible you could have given, the result of the loss of equivalence was that the Swiss gained business, while EU firms lost business
you have this the wrong way round: they are a bank based in the EU that was passporting their German (EU) license into the UK
in the near future they will not be permitted to operate in the UK as the UK will no longer accept their EU banking license