Just to add an extra question. Would the beginnings of the industrial revolution, starting in Britain, have had a place in the role?

Mods please tell me if I'm retarded here.

Being an economist and not a true historian, I tend to let Econ trump all other things (well, because it does).

I'd say ONE of the several reasons for the British empire was their knack for debt financing, ie using the Crown "guarantee" of debt issues to fund infrastructure and other development projects in the local currency, which carried the implicit guarantee of the mighty King.

It's extremely well covered in Ferguson's "The Ascent of Money" here http://www.amazon.com/The-Ascent-Money-Financial-History/dp/0143116177

The Bank of England's monopoly on money allowed them to issue new currency basically at will, and their superior enforcement on controls of compound interest rates encouraged banks to invest in government bonds, which allowed the government to dedicate a much larger portion of the national economy towards the financing of its navy than countries without these financial instruments. This led to an enormous military as well as slow economic growth throughout the eighteenth century. Without their imperial holdings, which were secured by the Royal Navy, their economy would have remained anemic throughout the 19th century as well.

Source: Prometheus Shackled

In short, it was two things:

1. Economic liberalism (the Free Hand) that made making money in UK territories relatively easy, due to deregulated markets with a real, independent judiciary. Basically it was worth it to invest in a business in a UK colony (compare to Russia today, or China, where you have no idea whether some bigwig will see you as a competitor and crush you illegally). Essentially, there really was freedom of sorts when you lived and worked in a British colony. The British knew how to create a minimal administration that left people to their own devices.

2. The British Navy was large and well-trained, and thus was able to keep shipping and trading lanes under control, relatively free of piracy a reasonable amount of the time, again making investment worthwhile, and keeping foreign powers from taking over easily.

Everyone seems to have covered Diamond and Crosby's work in regards to how this occurred so I'm going to talk a little bit about how location, coal, and New World assets helped give the British a boost to becoming the British Empire.

Prior to the 17th and 18th centuries British production of cotton and other goods were considered too expensive and lower quality which prevented them from being active within the Indian Ocean trade network that included China, India, Africa, and others in that same area. However, British assets in North America (access to more wood, land for growing cotton, etc.) allowed for more production of goods and a wider market while the introduction of slavery meant that labor costs remained low. Additionally, this access to what seemed to be an infinite amount of resources meant that population limitations put in place by, what Robert B. Marks refers to as, the "biological old regime" were diminished. In short, more food=more production while other areas, such as China, were forced to keep producing at the same rate due to a limited number of resources.

Now, this is all fine and dandy but where things really began to kick off for the British is with the discovery of easy to access coal (near a highly populated area and right on the surface.) China also had coal but it's location was too far from a major city to make it feasible to mine. Once the British began using coal to create superior iron, ships, etc. all that was left was for them to use force to open and control trade networks previously closed to them, which in-turn increased their wealth which led to the Opium Wars and imperialism, among other things.

Of course there were other factors that led to the success of the British in creating their empire, such as the Seven Year's War, but to go into all of theses things would almost be endless. I will admit my knowledge of this is skewed towards how the British influenced the Indian Ocean area and Asia but it should at least provide some added insight. A good book for this if you feel like reading a little more is Mark's The Origins of the Modern World: A Global and Ecological Narrative from the Fifteenth to the Twenty-first Century, it's fairly short (especially compared to Diamond or Crosby) and provides a decent overview of the topic.

Did the Personal Union with the Netherlands or Georgian Kings being HRE Electors grant any benefits to British imperial growth?

Mainly, it was the same way the Portuguese were able to establish a colony and somewhat maintain rule in a territory (Brazil) that was ninety (considering the total area after the territorial expansion imposed by the Bandeirantes scouts, disregarding the Treaty of Tordesillas borders) times bigger than Portugal: naval superiority (although Britain's naval power was far greater than Portugal/Spain at the time).

I could say some more things about the Portuguese colonial expansion that could relate to the British, but I won't say anything that I'm not sure about.

Just to add a couple interesting sources to what's been said: A small island does not mean a small population. England was insanely overcrowded in 1700s and beyond because of the massive increase in agricultural production at the beginning of the Industrial Revolution.

I recommend The Ghost Map as well as the beginning of The Fatal Shore for interesting information about how the explosion of population affected health and sanitation (the former) as well as law and colonialism (the latter).