Why did Britain develop an Empire?Watch
It's a well known historical debate surrounding economic, political/strategic and civilising forces. What would you say the reasons are for the development of the empire?
From there Britain moved into the Caribbean, but this came from war with Spain more than being a simple land grab - the root of much of Britain's successes lie in European wars that Britain came to dominate; so Gibraltar is an example of this, as was St Helena (where Napoleon died), so is Jamaica I believe, and a load of the North American colonies in Canada and the US. And Egypt which was a protectorate.
And there are places with a much lengthier historical association with England or Britain, English intervention in Ireland stretched back all the way through the middle ages. Claims on Newfoundland go back to the Tudors.
Obviously there are a humongous diversity of reasons that countries joined, some like Lesotho and Botswana asked to join, as did Malta during the Napoleonic Wars. Britain filled the power vacuum in India after the collapse of the East India Company - again it wasn't about mindless expansion although this certainly came into it later in the 19th century when jingoism went a bit nuts.
But to answer the question more directly i'd suggest that our being an island nation has something to do with it, we required a strong navy, and having a strong navy made it possible to maintain a strong empire - its sort of circular. But European war was the main drive, if Britain didn't have a global presence then France, Spain and the Netherlands would have had a colossal advantage.
Australia and New Zealand are somewhat comparable to the USA; Hong Kong is another example of the results of war, or more directly a result of trade i.e. Opium Wars (again the navy being central to the Empire because of trade).
But this isn't my area of expertise at all, i'm much more into the Medieval period - hope it helped though. Unfortunately the study of the Empire has been reduced to redundancy by the reactive left that seem adamant to see it as one single event that occurred for strict reasons that go against our 21st Century moralistic interpretations of the world and thus must be condemned without thought.