How far did Romans come when they invaded Britain?

The Romans had an empire, whereas the Greeks did not. The ancient Greek society consisted of several city-states, each under their own laws. The only time they united was in a time of crisis. When the crisis was over, they all went back to their own territories. The closest thing to a Greek empire was the conquests of Phillip of Macedon and his son, Alexander the great, but at Alexander's death the "empire" simply was divided and crumbled. The Greeks did have colonies in southern Italy, but they were colonies of Sparta, a city-state. In contrast, the Romans entered a territory, sometimes sent settlers there, and ruled the territory under Roman law, thereby attaining an empire.