The United Kingdom isthe name of the country that consists of Great Britain and Northern Ireland. Its full name is "The United Kingdom of Great Britain and Northern Ireland."
Great Britain is the name of the island northwest of France and east of Ireland that consists of three individual regions: England, Wales and Scotland.
Therefore,
England is part of
Great Britain, which is part of the
United Kingdom, as are Northern Ireland, Wales and Scotland. The South of Ireland is an independent Republic also known as Eire.