Divine ordination
Throughout the text, Dryden credits the events which are unfolding to divine ordinance. God is the unifying force throughout all the chaos of 1666. If God sees fit to make England suffer, He is entitled to do so. Beyond that, however, the British are of the perspective that they have God's blessing, so if He is making them suffer it is because He is purifying them for something greater which He has in store for the nation. The King of England is God's representative, so his leadership is revered and almost worshiped because he will best understand the will of God for his people.
Rivalry
The Dutch and the British are enemies in the truest sense of the word. By their mere existence, they are encroaching on one another's dominance. William III wants to be established as the global superpower for his colonization and spice trade, but Charles II is looking for military superiority and wealth. The two are incompatible with one another, so they inevitably must war with one another until one cedes final dominance to the other. This rivalry motivates all of the two nations' energies for the first two thirds of the poems.
Tragedy
After the war, the British are trying to recover from their losses. Ships need rebuilding. Widows need comforting. And the king's storehouses need replenishing. Tragically, though, they are instantly attacked in a different form when the plague breaks out in London. Since the rich can afford to pack up on a dime, they mostly escape to the countryside and avoid contagion, but the commoners are not as fortunate. Reeling from a massive population dive, the nation still doesn't catch a break because the fire breaks out in London. Most of the city is devastatingly consumed by the flames, all the way to the Thames. Again, the Parliament and the wealthy are protected from the fire, but their subjects are now fewer and fewer in number. These people who rejoiced in their military conquest and global dominance turn around to find themselves on their knees due to plagues and natural disasters. From the height of glory to the pits of loss, England feels the full extent of true tragedy.