The map below shows teritory that was at some point controlled by the British Empire (in the traditional pink) — the thin white lines show the modern country boundaries. Needless to say, the definition of ‘controlled by the British Empire’ is not universally agreed upon. I’ve tried to produce a balanced map that will lead to few disputes, but if you disagree feel free to contact me. Thanks to James Alcock for pointing out some unintentional omissions.
If you want to know more about the British Empire, the definitive book is Lawrence James’ The Rise And Fall Of The British Empire. Unlike most books on the British Empire, it is remarkably unbiased, and worth a read wherever you live.