It would be interesting I think to look at the story from the beginning and examine how the Empire happened, and how it expanded over time.
It's a common misconception among many people (particularly Americans) that Britain had some grand master-plan to dominate the world and set out to conquer and rule nations. Nothing could be further from the truth. The British Empire occurred almost by accident and as a result of trade.
It's a story of explorers, entrepreneurs including miners, shipping and international trade.
The story begins close to home, in Ireland. Where Britain takes control of Ireland and gains its first colonial possession. At that time, Britain was at war with the Catholic nations who had all sided against Britain that was now a protestant country. Ireland being a Catholic country naturally posed a threat to Britain. Britain built up its naval power and by the 17th century, Britannia ruled the waves having defeated the Spanish Armada.
With Britain's naval power and dominance of the seas it was able to explore continents in the 17th century which lead to the first colonies being established in America and cotton, sugar and tobacco plantations being established which brought much wealth to Britain. By the latter part of the 18th century, after the colonies gained independence, the British Empire moved eastwards and took control of the East India Company from the Dutch which became the British East India Company. This enabled Britain to control most of the trade routes between East and West, particularly the lucrative silk, tea and opium trade with China. At this stage it was still private enterprise under Royal Charter. There was no involvement by the British government.
As the situation got more complicated in India and British interests were being threatened by feudal warlords, the British army was called in and eventually the British government established administration over large areas of India which was then incorporated into the British Empire along with several other countries in South East Asia. By the early part of the 19th century Britain was at war with China over disputed trade routes and China's ban on opium. Britain defeated China and gained Hong Kong from China on a 100 year lease. By the 19th century the British mining operations began in Africa, the main operation being started by Cecil Rhodes in South Africa. Rhodes and the other mining operations generated so much wealth from diamond mining that he established a town which developed into a small country, of which Rhodes eventually became Prime Minister. These parts of Africa were also added to the British Empire.
It was during the 19th century, in the Victorian era that Britain started to experience social overcrowding in towns and cities as the industrial revolution gathered pace. This obviously brought with it many social problems including higher levels of crime. As Britain's prisons got fuller, they decided to establish a penal colony on the barren continent of Australia which had been added to the British Empire a century earlier but never fully colonised or used.
By the 20th century, the British Empire had moved into the Middle East as the Empire now needed oil instead of coal. British oil companies were started which took control of most of the oil in the Middle East which enabled Britain to continue to rapidly expand and grow its economy. At that time peace had finally established with France, Britain's longest rival and the other main competing imperial world power after more than four centuries of war. However a new war was on the horizon which test and push the power of the British empire to its limits. It was of course, the first world war, in which Britain and France fought a common enemy together which began in 1914 and ended in 1918.