Pretty much every country has at least some options for opening a bank account for non-residents. TSB has an account for EU, non-UK residents for instance, that gives you a normal UK checking account with a visa card:
Yup, but you have to be elsewhere in the EU. You can have a non-resident bank account pretty much anywhere, but you either have to visit the bank's branch office, or be trusted in any other way (residing in a jurisdiction that's trusted, or be a bank's customer elsewhere)
https://www.tsb.co.uk/current-accounts/faqs/opening-a-curren...