I was told by a friend that all the empires fell primarily because of a giant wealth gap in their societies that weakened them from outsiders or made the general populace rebel (usually both). Obviously he was saying this because of his political stance, so I have no idea if that claim is right, but it made me start wondering what the economic landscape was actually like for the great empires and did it play any large part in their downfall? Were there any similarities between their economies?
Firstly, Greece was never a "major Empire" unless you are talking about Alexander's Empire specifically, which fell because he died without a clear heir.
I won't address Rome, because while I've read books and so on about Rome, I studied modern and early modern history, not classical history, so I don't feel qualified to give a good answer.
I will comment on Britain though.