…they were probably already famous in the UK for one reason or another. You just might have forgotten about them.
Anyway, now's your chance, thanks to Buzzfeed, to try to work out where you saw various famous British (and Irish) actors who are now/were in Game of Thrones. Some strange choices: obviously Jerome Flynn was big in Soldier Soldier, because it was his singing in that show that enabled him to have a pop career, but they went with one of his pop videos instead (and not even 'Unchained Melody'); Julian Glover and Charles Dance have had huge acting careers so Ali G In Da House isn't what I would have gone for for Dance and Indiana Jones and The Last Crusade offered Glover a much bigger role, at least (although I do love his live performance of Beowulf); Aiden Gillen was obviously hugely famous from Queer As Folk, not Shanghai Knights; and if you've seen Elf - which everyone has - that's not the Peter Dinklage moment you'll best remember.
But it's still fun to watch and look back at the shows they did pick. Particularly the one for Rory McCann (the Hound). That, I wasn't expecting.