Greetings! This is a most interesting question indeed, and it does expose an equally interesting aspect of not only British imperialism, but European empire-building as whole: the role (and importance) of religion in colonial ventures. Whilst obviously the answers will differ for each empire, it is rather fortunate that OP has specified the British Empire, and even more specifically the contrast between the British Raj (modern day India, Pakistan, Bangladesh, Sri Lanka and parts of Burma). Note that this response will cover the general patterns of religion's interaction with (or lack thereof) the colonial system, and bring up potential case studies where appropriate. Let's begin.

Missionaries and the "Imperial" Mission

"[A missionary is] a religious Englishman with a mission to offend the religious feelings of the natives.

- Lord Salisbury, British Prime Minister (r. 1885-1886, 1886-1892, 1895-1902)

Missionary work was not a new phenomenon in Crown-controlled India (or prior to that, the rule of the British East India Company), nor was it a particularly novel introduction to the West African shores and societies. After the 1790s, a swathe of missionary societies were founded to recruit and dispatch a corps of "spiritual messengers" to the non-Christian world. Among them were the London Missionary Society (1795), the Baptist Missionary Society (1792), and the Anglican Church Missionary Society (1799). After the long war and victory over Napoleonic France in 1815, many missionaries felt that the survival of Britain held a double belief, which John Darwin outlines below:

"The arduous struggle with France (1793-1815) and the social strain it imposed made moral cohesion seem all the more urgent. Its victorious conclusion bred a double belief: that Britain's survival was part of God's plan and that this imposed on its people an evangelical duty."

This new sense of "religious duty" came as new worlds from the late eighteenth century were 'opened up' to Europe: India, China, the Pacific, as well as the interiors of West and South Africa. It was not uncommon for members of these missionary societies to settle in newly ceded or controlled territories, and to attempt to spread the "word of God" amongst the people who had previously controlled the land. In West Africa, much of this work rested on the shoulders of 'Liberated Africans' from Sierra Leone, among them the Anglican missionary statesman Samuel Ajayi Crowther (1807-1891), a Yoruba from what is now western Nigeria.

Western Africa was a prime location for the spreading of Christianity alongside the expansion of empire. Sierra Leone was this location's "nexus", where missionaries could make good use of the trade links from Freetown along the coast, the ties formed by the Yoruba populace, and a ready supply of Christian believers. Of course, as the empire in Africa developed and more territories came under the control of the British government, the concerns raised by missionaries in their line of work became something of a nuisance and a tool for imperialists across the continent. In West Africa especially, local tribe rulers knew that converting to Christianity and accepting the "guidance" of the missionary would invite further state-building with support from the British. On the other hand, committing oneself to the words of a missionary also meant committing one's spiritual allegiance to the country that missionary was a representative of (even though this was rarely official). The Lesotho ruler Moshoeshoe for example, encouraged conversion to Christianity amongst his people, but shrewdly refused to convert himself until he lay dying.

In other words, welcoming missionaries to a community was (in the case of Africa) often due to a number of reasons. Chiefly however, they brought with them the promise of external contacts, skills, information, trade, and diplomacy, but without external control. Missionaries of the early nineteenth century loathed the conquests of imperial territory, and thus their unarmed (and supposedly "peaceful") presence amongst an indigenous community was at least some reassurance that a British battalion would not be stopping by anytime soon.

Further, consider that prior to the arrival of British missionaries, West African societies (in a pattern not too dissimilar to other parts of the continent), had experienced ethnic divisions either to due internal fallout or external ones caused by European empire-building. South Africa missionary statesman Dr. John Phillip (1775-18510 expressed such a sentiment:

"The great bane of Africa is the minute fractions into which its tribes have been broken up by the Slave Trade; we have here materials for a viable building but nothing can be done towards it till the fragments are joined together. The Gospel is the only instrument by which this means can be accomplished."

So why was this success in conversion not replicated in India? That is where we are headed next.

The Company and Christianity

"We now know that with perfect safety our Christian government may assert its national faith without offence to either Mahomedan [of or relating to Islam and the Prohpet Muhammad] or Hindoo [sic]

- English churchman John Kaye, 1858.

Recall how we touched on the beginning of the 19th century being a "watershed" moment of sorts for missionary activity and evangelical zeal in the British Empire. The role that the East India Company's expansion into the Raj was a massive component of this rise in religious concern (and hopes) for the empire. Alongside the acquisition of large swathes of territory on the Indian subcontinent, white settlement in Australia rose significantly, and this coincided further with the expansion of the empire's interest into China (though this occurred to a far lesser extent and slightly later, starting in the 1840s). Such was the pace at which the British empire was expanding its influence (and in some areas control) in the early nineteenth century that the sentiments of clergymen and evangelists back home were often aligned to those of the "empire-builders" and imperialist advocates in Whitehall. The bishop of Stepney for example, declared that:

"The Imperial spirit in the State calls for an Imperial spirit in the Church."

A popular metaphor of the age proclaimed that wherever the Union Jack went, the cross was usually never far behind. Yet more often than not, the Union Jack had fewer obstacles to surmount in its planting than the cross, and that was particularly true in India. Imperial historian Ian Copland explores the value of India towards the missionary societies of the nineteenth century:

"For the church, India was an irresistible temptation - the quintessence of heathenism and home, therefore, to countless 'lost souls' crying out mutely for 'salvation'."

Yet before the Sepoy Mutiny of 1857-1859 and the establishment of "direct" rule from London thereafter, the British East India Company actively discouraged missionaries from entering their territories on the subcontinent. This discouragement was mainly due to the fear that missionary activity in such a vast religious landscape with hundreds of thousands (if not millions) of followers would incite suspicion from the local elites and populace that the British were trying to impose Christianity upon them. Ian Copland explores this curious paradox of a perceived "super-company" with direct control over vast tracts of land being so cautious not to upset the local religious groups:

"For all that the Company now reigned supreme in the subcontinent...its officials remained nervous, conscious of how few they were and how much they depended for their security on the collaboration of mainly Hindu native soldiers - a collaboration that hinged, it was generally believed, on the Company's promises that the religious and social status quo would not be tampered with."

In other words, to avoid stirring civil unrest over religious matters and proselytization efforts by Christian missionaries, the East India Company strictly forbade the entrance of evangelists and missionaries onto the subcontinent, and those who did manage to land in Company territory had to seek religious and political sanctuary elsewhere (for the somewhat logical fear of being associated with the missionary in question, should anything bad come from their activities). So for the first few decades of Company rule over much of India, the cross was barred from entering where the flag had been planted in a seemingly fragile collaboration with local elites and religious leaders.

Part 1 of 2