I'm looking for books about, or have good sections on the economy of the British Empire.
In particular I want to know what banking and monetary policy was like in the British Empire at different stages.
Did colonies coin or print their own currency or did they all use money printed by/on the order of the Bank of England? What about when colonies achieved Dominion status?
What were the major economic activities of different parts of the empire?
Also, was the Great Britain/the United Kingdom (depending on the period) ever afraid that one of their colonies would overpower the mother country economically or politically?
Any suggestions are greatly appreciated.
I have previously read some of the essays in The Oxford History of the British Empire and several of them certainly cover aspects of what you're asking. I haven't seen much on the monetary policy but most books will look at the banking and financing of the Empire. Not my favourite historian but Niall Ferguson has two books which may be of use to you - one called 'Empire - How Britain made the Modern World' and 'The Ascent of Money - A Financial History of the World' which might offer some recent ideas on to the subject.
It would help if you could narrow this down to a time period or specific relationship between a colony and the metropole.
For example, a contrast of monetary policy between Great Britain and Australia in 1900 is a vastly different world than that of Great Britain and the Raj in 1918.
Most of the books I've read on the British economy tend to treat the Empire as an afterthought. This is very unfortunate as there is a rich and interesting history there to be told.
I know this isn't quite what you are after but there are some books on certain companies that operated in the colonies. Merchant Kings: When Companies Ruled the World, The Sugar Barons, The Honorable Company on the English East India Company (I wasn't too impressed with this, at all, but there aren't many books that focus on this).
The first book in Jan Morris's Pax Britanica trilogy has some chapters on the East India Company and the Hudson Bay.
I say this because until the mid-19th century much of the British empire was run by corporations. The East India Company conquered much of India for profit. Hudson Bay company controlled Canada for a good while. That means until the mid-19th century there wasn't really much of a "monetary policy" to be had in regard to the colonies. Corporations (and sugar barons in some colonies) set economic policy. Britain helped enforce it (although often they didn't East India Company had their own army). For example, the East India Company issued coinage to be used in India until the 1860s. It was separate from the British government until the British government took it over.
This is all because British economic policy was pretty laissez faire for much of that time. Setting economic and monetary policy through out their empire wouldn't necessarily be seen as the government's job until fairly late in the empire's history. As to whether they worried about their colonies overtaking it? Unless you count the US, definitely not. England was the most industrialized nation in the world for quite some time. And had the most sophisticated financial sector well into the 20th century. None of the colonies were in a position to supplant it. The US was a threat, of course. But even then the US may have had factories but it didn't even have a bank to compete with British banks until JP Morgan, which is fairly late in the game.
I can tell you that the American colonies each issued their own paper currency. And coins circulating in the American colonies were as likely to be Spanish dollars as British sterling (hence we use dollars not pounds). In Canada, money was always an issue as there was never enough actual currency. In the early 19th century banks started issuing paper currency just like the US. In the mid-1820s the UK tried to put their foot down and have all of the colonies firmly on British sterling but it didn't really take.