The continent of South America looks as if it managed to escape the attentions of the British Empire. However, this was more because the British didn't need to exert formal control over the countries and peoples of this continent. The Monroe doctrine imposed by America, served British interests quite well enough. The doctrine made it clear that the United States would not tolerate foreign meddling in the Americas. This policy meant that Britain could get all the benefits of trade and investment in South America with very little of the administrative costs. In addition, it could be reasonably safe in the knowledge that other European states wouldn't be able to steal the markets through annexation. Britain had very strong commercial links with South America, especially with Argentina. In many ways, the influence and power that Britain could hold over the policies of the individual South American states meant that they could almost be termed as being part of Britain's informal empire. The islands in the region that were formally annexed were done so mostly out of strategic naval considerations.
Although, Hektor Fuster argues that the British were not quite as removed from South American nation building and imperial adventures as it may have seemed. Read his article on The British role in the independence of South America from Spain.