This is an excerpt from Will Kymlicka's Contemporary Political Philosophy: An Introduction discussing utilitarianism:
A less extreme form of indirect utilitarianism is what [Bernard Williams] calls 'Government House' Utilitarianism. On this view, a small elite would know that utilitarianism was the right moral theory, and they would employ utilitarian decision-procedures to design utility-maximizing rules or institutions. The cast bulk of the population, however, would not be taught to believe in utilitarianism. They would be taught to view social rules and conventions as intrinsically justified. (This is called ' Government House' utilitarianism since it seems to have been the view of some British colonial officials in India and other British Colonies: the British officials would understand that rights are simply ingenious devices for maximizing utility; the natives would be taught to think of rights as intrinsically justified and inviolable). [Emphasis Mine]
Moral philosophy aside, I'm curious about the veracity of the historical claim. Was an esoteric utilitarianism ever an established policy in British colonialism? Was it ever the de facto policy, if not formal one?
You're jumping into a bit of a snake pit here, as the motivations behind British Imperialism generally have been hotly debated by historians for decades, with historians of British India often playing a prominent role in it. Generally, which policies, motivations, and justifications a given historian justifies will depend on what type of historian she/he is. Therefore an economic historian might emphasize the role of the desire for profit in East India Company (EIC) and India Office policies, as well as British policy relating to India more broadly. Of course a political or military historian might see things differently, as could people working in Postcolonial Studies or Subaltern Studies, with their motivations in emphasizing specific policies ranging from objective research, to apologetics, to ideology.
It is my view that British policy in India under the EIC, especially before the late 18th Century, had very different motivations than in the 19th Century, particularly after the [1857 Rebellion] (https://en.wikipedia.org/wiki/Indian_Rebellion_of_1857). While national aggrandizement certainly played a role under the EIC, the desire for profit (both in terms of dividends for the EIC share holders and the wealth accumulated by individual EIC administrators and military officers in India) and realpolitik style power accumulation played a prominent role in directing policy during both war and peacetime. Ideology began to play more of a role over time, and sometimes against the will of EIC officials, who notably attempted to prevent missionary activity in their dominions as they saw it as a threat to the status quo.
In the 19th Century ideology began to play a more prominent role, partly as a result of the influence of Evangelical Christianity, which took a more active political role than mainline Christianity in colonial policy (including a prominent role in the abolition of slavery) and emphasized missionary activity to a greater degree. This, combining over time with emerging national and imperial narratives, political and economic theories, and eventually racial theory led to the ideas like Britain's 'Civilizing Mission.' Nonetheless, it would be foolish to think that profit and the desires for power and security did not play a role after this point, and many historians argue that factors like these remained the most important influences on policy.
I am not an intellectual historian, but the development and spread of utilitarianism did coincide with the development of the idea of a 'Civilizing Mission,' and considering its influence in Britain more generally at the time I would not be surprised if it did influence certain individuals who drove policy relating to the British Empire. It is important to note that how much influence these 'policy makers' had on policy is also a subject of debate, as events and individuals on the periphery had just as great - if not more - of an influence of actual imperial policies in the 19th Century. A classic text that is part of this debate that you might consider reading is Africa and the Victorians: The Official Mind of Imperialism by Robinson and Gallagher. Checking their index and looking for mentions of utilitarianism might be a good idea. If you're interesting in researching this topic in depth I would suggest a trip to the Asian and African Studies Reading Room at the British Library, which has the records of the EIC, India Office, and other colonial records.
No, "Government house" utilitarianism was a term facetiously used by Bernard Williams to describe Sedgewick's defense of utilitarianism in "The Methods of Ethics."
Thus, the Utilitarian conclusion, carefully stated, would seem to be this; that the opinion that secrecy may render an action right which would not otherwise be so should itself be kept comparatively secret; and similarly it seems expedient that the doctrine that esoteric morality is expedient should itself be kept esoteric. Or, if this concealment be difficult to maintain, it may be desirable that Common Sense should repudiate the doctrines which it is expedient to confine to an enlightened few. And thus a Utilitarian may reasonably desire, on Utilitarian principles, that some of his conclusions should be rejected by mankind generally; or even that the vulgar should keep aloof from his system as a whole, in so far as the inevitable indefiniteness and complexity of its calculations render it likely to lead to bad results in their hands.