The U.K. cannot hope to retain its financial passporting privileges if it pursues a so-called "hard Brexit" that involves a withdrawal from the European Union's single market, according to Valdis Dombrovskis, the vice president of the European Commission.

"The issue is quite clear. EU passports are linked to the EU single market. So if the intention of the U.K. is also to leave the single market then indeed U.K. financial institutions cannot have EU passports," declared Dombrovskis, who is also the European commissioner for the euro and social dialogue, speaking from Brussels to CNBC on Thursday.

"Those things indeed come together, so then the question is basically if you can rely on equivalence in certain sectors or establish sufficient presence within the EU to maintain an EU passport," added the former Latvian prime minister.