I don't know when to say "Britain", "England", and "United Kingdom".
The "United Kingdom" is actually a short form for "The United Kingdom of Great Britain and Northern Ireland". It is an independent country (in the same way as France or the USA) but is made up of four smaller countries; England, Scotland, Wales, and Northern Ireland. So the "United Kingdom," is like the USA, in that the four "countries" are like states. "Britain" is not really a reference to a country; it’s a landmass. It is the largest island in the cluster of islands that make up the British Isles and contains "England", Scotland and Wales. "England", like Wales and Scotland, is often called a country but it is not an independent country. It is the largest country within the United Kingdom both by landmass and population, and its capital London is also the capital of the "United Kingdom." This is probably why "England' is sometimes used to describe the whole of the "United Kingdom". So in quick summary: The "United Kingdom" or UK – a country that includes England, Scotland, Wales, and Northern Ireland. "Britain" – an island. "England" – a dependent country within the "United Kingdom". I hope this helps.