> And an empire with the world's largest military, ruled by a despotic aristocracy which had made most of its money from slavery, drug running, and land + resource grabs in distant countries.
Calling the ruling class of the British Empire a despotic aristocracy is a very big stretch, or better a contradiction. Despotic regimes have non-existent or vestigial aristocracies, e.g. the Ottoman Empire or most Chinese dynasties. The Russian Empire had an aristocracy had what looked kind of like a Western European aristocracy but a service nobility functions very differently from one where the nobility have independent power bases. For much more on this Francis Fukuyuma's "The Origins of Political Order" is excellent. In brief there are three political classes in pre-modern societies, the monarch, the high nobility and the gentry/bourgeoisie. The peasantry are irrelevant because they can't coordinate so their numbers are moot. A strong civil society with rule of law that binds the king/state as well as other actors emerged only in Western Europe. If the law binds the king he's no despot, and it did. In Britain, Scandinavia and the Netherlands the king allied with the gentry, in France and Iberia, with the nobility but their power was constrained.
Imperialism did contribute to the power of these states, more to the noble class than the country as a whole but it was not where that power ultimately came from. It came from growth in economic productivity and the organisational capability it made possible. The British Empire was not planned, it was the product of absurdly huge differences in capability. It was acquired over centuries by men on the spot chasing personal glory and advancement.
This is not to deny the slavery, drug running and land and resource grabs but they are frankly secondary. The Royal Navy was the force behind the destruction of the slave trade. The British parliament abolished slavery within the British Empire over the protests of some very rich and well connected domestic interests. The opium trade and the immiseration of India were enormous crimes but the capability preceded the crimes and was only possible because of it. Britain's wealth was not built on the Empire, it was built on trade, commerce and industry.