Great Britain is a geographical term for the largest island in the British Isles, comprising three countries: England, Scotland, and Wales.
England is a political entity—one of the four constituent countries of the United Kingdom (UK). It covers the central and southern two-thirds of the island of Great Britain.
The sovereign state is the United Kingdom of Great Britain and Northern Ireland (UK). It includes:
So: England ⊂ Great Britain ⊂ United Kingdom. Never use "England" to mean the UK or Great Britain—it excludes Scots, Welsh, and Northern Irish.