It's nice you mentioned invading Germanic tribes, that's why purists might even deny Italy and Greece any connection to their glorious predecessors.
France and UK have negligible ethnic connection to Romans or Greeks.
Here is the difference with India - unlike Europe here ethnic mix did not change much and modern states may claim historical legacy freely. The same population, the same territory.
In Europe Italy and Greece have the same territory as Roman empire and Greek city states but population might had changed ethnically significantly over the centuries, not speaking about Christianity which was not existent in ancient societies.
About China I would recommend you to read any history book, for example John Keay's History of China and you will understand where your question or statement is fundamentally flawed.
That's a popular line among the European far-right. It does not, however, have anything to do with reality.
The reality, of course, is that most empires succeed to some extent in imposing their culture on their colonies, and in some measure adapt their culture to reflect that of their colonies.
And, of course, cultures evolve over time, to the point where they become unrecognisable as the ancestor culture. To say that modern Greece or India has any claim to the monuments located there - other than the geographic fact that they are located in their jurisdiction - is vaguely silly. Just as it is vaguely silly to suppose that Germany has some claim to the merits of the Hanseatic League.
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.