I would say that hierarchy was embedded in the British Empire in a myriad of different ways. Indeed, note that British society was itself a deeply stratified one, as the older aristocratic culture of the landed gentry was reshaped and transformed by industrialization's impact. With the Industrial Revolution, you can observe the rise of the industrial class system, with its divisions between the working, middle, and upper classes (divisions based on one's wealth, income and one's role in the process of production). You can also note the existence of a religious hierarchy (with the Anglican Church occupying the top spot), not to mention ethnic hierarchies and tensions, particularly surrounding the subjugation and exploitation of Ireland.
I begin this discussion with the British Isles because it is Great Britain itself that stands at the center of the picture of empire, imposing its own power and influence over the rest of the world. Thus, to truly understand the nature of any imperial hierarchies, it would be useful to contextualize this discussion with an awareness of hierarchy as it fits into Britain's own political and economic system. Indeed, note the degree to which, economically speaking, the British Empire was itself culpable for imposing a system of capitalist and industrial exploitation, by which the British would extract raw materials from the Empire, and then sell back to it those manufactured goods produced by the British industrial system.
At the same time, note that any discussion of the role of hierarchy within the Empire needs to also be aware of the existence of parallel hierarchies, both native and imperial, coexisting with one another. You can observe an example of this in India, which had experienced millennia of history and civilization long before the arrival of the British East India Company, and had evolved a system of political and social stratification centered around the Hindu Caste System. Even under British imperial domination, this older system did not disappear, but was rather enfolded into this British imperial system (with much of this older hierarchy remaining intact). Of course, it should be noted, the Empire had a very heavily racial and racist dynamic, with the imperial agents existing as very much the dominant political class, but basic pragmatism often required that they rule with the assistance and cooperation of local elites and rulers. In this sense, you can observe a situation by which local elites and power structures remained intact, even as they were suborned under the British imperial system, and ultimately subservient to British interests.