How did the British Empire come to be?
The British Empire came to be in fits and starts and at times almost by accident.
Not counting Ireland, the British Empire began in the Americas. The desire to colonize in the Americas came about because of the economic and military power that Spain was deriving from its empire there. The taking of India, the "jewel in the crown" of the British Empire came about indirectly. The first steps into India were taken by the British East India Company and it was only after a very long time that the British government actually took over. At the same time, other parts of the empire were falling into place through wars (Hong Kong) or simply through "discovery" (Australia and New Zealand). Later imperialism (Scramble for Africa) was motivated at least in part by a desire to "civilize" the rest of the world.
So, we can't say that the empire came to be as part of some grand plan. Instead, it came together gradually, generally because of some mix of economic, political, and religious reasons.