The United Kingdom of Great Britain and Northern Ireland is a country on the east side of the Atlantic Ocean and just to the west of the European continent. It is sometimes referred to simply as Britain or “the UK”.
The United Kingdom is comprised of four countries.
Northern Ireland, the fourth regional country of the UK, is separated from Great Britain by the Irish Sea.
It is important to note that the Republic of Ireland, although also located in the British Isles, is not part of the United Kingdom.
These locations are, of course, where the entirety of the Harry Potter series takes place.
The identities, composition and government of the current and former countries or regions of the United Kingdom, Great Britain and the British Isles have a very long and complicated history.
"Great Britain" only comes up once in the Harry Potter series - in the title of one of the books that Hagrid has consulted in the Hogwarts Library: Dragon Species of Great Britain and Ireland (PS14). It is also mentioned in J K Rowling's Pottermore writing on the Magical Congress of the United States of America MACUSA (Pm:NorthAmerica). The United Kingdom is only referenced in her Pottermore writing on the History of the Quidditch World Cup where "the known existence of a violent Pure-blood tendency in the United Kingdom" is not very flattering. The word Britain on its own appears several times in canon. The individual countries of the UK, as they do in many Muggle sports competitions, have their own separate Quidditch and wizard sports teams - specifically from England, Scotland and Wales (GF5, QA8, Pm:Quidditch). The British and Irish Quidditch League, however, fields teams from both the UK and the Republic of Ireland - so you do wonder whether Ministry of Magic control extends over the entirety of the British Isles, or if the Wizarding World has unified Ireland. Given the history and politics, neither of those feels very likely. --td
From the Web
British Tourist Board: Visit Britain
The National Trust for Places of Historic Interest or Natural Beauty
Wikipedia: Terminology of the British Isles
Ordnance Survey: The difference between UK, Great Britain and the British Isles