>Is it fish caught in that same day like you can get in any Greek taverna in the Cyclades?

Yes. There's huge amount of fish bought in from inside the UK from Cornwall/Brixham etc etc. Never mind all the stuff that's air freighted here.

>Or frozen fish brought in from half a continent away?

All fish in the EU is frozen anyway [1].

1. https://www.food.gov.uk/business-guidance/freezing-fish-and-...