I'm from America, but I did teach social studies. The official title is or was when I taught school the United Kingdom of Great Britain and Northern Ireland. England is a part of Great Britain along with Wales and Scotland. The United Kingdom also has as part of its sovereign territory Gibraltar, the Falkland Islands and several other areas throughout the world
The Republic of Ireland which is in the southern part of the island is NOT part of the United Kingdom.
When the colony of Jamestown was founded, Scotland and England were two separate sovereign countries. That changed at the death of Queen Elizabeth the first when the King of Scotland was also in line for the throne of England. The two kingdoms eventually merged but remain two separate regions called countries, but they are not sovereign countries. That is why in history the term England is used for the period of English history up until the time of Queen Elizabeth I death.
In world language the term United Kingdom replaced the term British Empire during the 1950's as the Commonwealth was created replacing the Empire.
Jamestown was named after James I of England and VI of Scotland. The two kingdoms were in personal union, that is, same king, different governments through the 17th century, after James, King of Scotland and the cousin (once removed) of Elizabeth I, succeeded her in 1603. The term Great Britian gradually and unofficially came into use(Less Britain is the Duchy of Brittany, on the continent).The government of Scotland was in financial difficulties in 1707, and agreed to unite governments, it was from then officially the Kingdom of Great Britain. Brittanium is the ancient name, used by the Romans, of celtic derivation, Prythein is the welsh.
In 1801, the government of the Kingdom of Ireland, conquered and reconquered by the English over the centuries, was combined, it was from then the United Kingdom of Great Britian. In the 20th century, most of Ireland became a self governing dominion, and gradually fully independant, the northern counties, with a large population of protestants, remains part of the UK.
The formerly independant Principality of Wales (Cymru in welsh)is is the remnant of the celtic people who formerly also occupied the whole of England, before the Anglo Saxon invasions following the withdrawall of Roman troops. It has been united with the Kingdom of England around 700 years.
There is also the Island of Man, formerly a Kingdom. There were once many small kingdoms, Kent, Wessex, Wight, Mercia, Deira, Anglia, York, Essex, Lindsey, Hwicce, Magonsaete, etc. were united in the Kingdom of England. Cornwall was not yet a part of the kingdom of England at the time of the norman conquest, it long kept it's own celtic language.
The Channel Islands, Guernsey, Jersey, Alderney and Sark, are the remnants of the Duchy of Normandy, part of the UK, but not part of England, likewise the island of Lundy.
Scotland, Wales, and Ireland were once also composed of many small kingdoms(sebregulae). The Orkneys were once part of the kingdom of Norway, and came to Scotland as a dowry.
The Kings of England held the title Lord of Ireland, (though they usually didn't control more than a part) then from Henry VIII to George VI, King of Ireland.
The royal lineage can be traced from the Windsors through the Saxe-Coburg and Gothas, the Hanoverians, the Stuarts, the Tudors, the Plantagenets, the Normans, Danes, and Anglo Saxons, the kings of Wessex, to the 6th Saxon invaders, Hengist and Horsa, to the god Odin.
Under king Canute, the kingdoms of England, Norway, and Denmark were united. Under the Normans and Plantagenets, the Duchies of Normandy and Aquitaine, and the Counties of Anjou, Gascony, and Poitiou were united with the kingdom of England. The plantagenets (and to George III) claimed to be kings of France, and were on occasions recognised. Queen Mary I's husband Phillip Habsburg had the title King Consort of England, and was also King of Castile, Leon, Aaragon and Navarre(and later Portugal) and Duke of Burgundy, Brabant, Luxemburg etc. The Hanoverians were also Electors of Hanover in the Holy Roman Empire.
To me, the term 'the British Isles' refers to all above (including Ireland) except the channel islands, it is a geographic/cultural term, not just a political one. Likewise 'british Literature' includes Irish.