Rome and Greece are Mediterranean civilizations. Yes, Rome annexed much of Europe into its empire but through war - Western Rome fell in part due to Germanic groups fighting against that occupation, and the Romans weren't able to occupy all of the British Isles.

So, when did European powers outside of what we can consider the 'core' of Rome start to identify with Greco-Roman history? Was it immediately after the fall of Western Rome, due to the influence of the political elite and religious (Papal) power that Rome created in these areas? Or did it take time for that identity to be claimed?