There are some fundamental differences between Great Britain, England and UK(United Kingdom), these differences can be easily understood by the following clarification:
United Kingdom
In fact, the United Kingdom is a country itself. It includes Scotland, England and Northern Ireland.
The Official name of UK is "United Kingdom of Great Britain and Northern Ireland".
Peoples consider that England, Wales, Scotland, and Northern Ireland are independent countries but in reality they are only a part of the United Kingdom.
Great Britain
Great Britain refers to an island that consists of three somewhat autonomous regions that include England, Scotland and Wales.
It is located northwest of France and east of Ireland in the Atlantic Ocean.
England
England is sometimes wrongly used to refers to the whole United Kingdom or to the the island of Great Britain.
In fact, England is the only part of Great Britain.