The Taiping Rebellion, which is recounted in Jonathan D. Spence's God's Chinese Son, took place in China in the mid-nineteenth century. It was led by a charismatic Chinese man who came to believe he was the younger brother of Jesus and that God wanted him to create a "new Jerusalem" in China.
In seeking to understand how the British viewed this rebellion, grasping the context of British Imperialism in China at the time is critical. This was an age of European empires who were establishing trading rights and privileges as well as colonies across the globe. Further, the major European powers were in a contest with each other for dominance through the riches that imperialism had to offer.
Subsequently, as their interests were not political outside their nation, this rebellion would have been a matter of "Chinese domestic politics" to the British. Their policies regarding it would have focused mainly on the need to maintain their trade and commerce privileges without interruption.
Officially, the British position was one of neutrality between the existing government and the rebels. For the most part, the British considered this to be a civil war between Chinese factions, while regarding the rebels as agitators. The British were under general orders to use force only to protect British holdings and interests in the region. In practice, however, the "neutrality" of British forces in China was questionable, and seemed to exist in a permanent "grey area."
In many cases, there were cities in which the British had large trading posts or compounds exclusive for their use. As these areas and the troops protecting them were ultimately closely intermingled with targets for the rebels, efforts to attack only the government and leave the foreigners unaffected were usually unsuccessful. Time and again, British forces engaged the rebels when they felt the rebels were too close or were in some way, directly or indirectly, threatening British interests.
In summary, the British viewed this rebellion as a civil war and largely a matter of Chinese domestic politics. If it didn't interfere with their trade, they would have remained uninvolved. In practice, though, the unrest caused by the rebels often led the British to interpret their instructions to remain neutral quite liberally, meaning they did not hesitate to engage the rebels in combat whenever they felt it necessary.
Overall, the British showed the same chauvinistic attitude that was common for that time, meaning that the needs, desires, and goals of both Chinese factions were consistently overridden by the pursuit of British self-interest.