‘Divide and rule’ (or ‘conquer’) diplomacy aims to disunite the opposition, the better to control it. The ancients were masters of it. So is the EU, unlike the UK.
In the 4th c bc Philip II of Macedon played the game very skilfully as he plotted his conquest of Greece. Taking full advantage of the fact that the Greek city-states spent most of their time quarrelling with each other, he offered the hand of friendship to some, used his powerful army against others, and all the time offered peace terms to Athens. Wisely, he left Sparta alone. (When he told them they would be slaves for ever if he conquered them, they laconically replied ‘If’). He eventually turned Greece (minus Sparta) into a federation of states ruled by Macedon.
Julius Caesar adopted a similar strategy to conquer Gaul (59-50bc). The southern coast of Gaul was already a province, and Rome had made alliances with adjacent tribes, though they were not stable allies. The tribes further north, in Britain, and in Germany, presented the major problems for Caesar, especially Germans, keen to get a foothold in Gaul as squabbling Gallic tribes called on their help.
Caesar’s strategy, then, was to show the Gallic and Germanic tribes who the military master was and play one off against the other, with acts of clemency to some who had turned against him, genocidal slaughter against others. Slowly but surely he picked off the various tribes. A major revolt raised by Vercingetorix in 5bc came too late.
However, for divide and rule to work, there needs to be a central power-base doing the dividing. That is the EU, whose means of dividing and ruling is the euro. Look what happened to Greece. Member states may grumble about closer integration, immigration and so on, but they all need good deals on budget day. Consider its shifting positions on Brexit: a deal one day, none the next. And the UK? In the absence of a powerful central authority on the Brexit question, there can be neither ruling nor dividing, only chaos. That suits the EU just fine.