The isles off the north west coast of Europe were settled during the stone age and their peoples have exchanged genes and ideas since that time. In 7000BC one could walk, on dry land, between the countries now known as France and England, but one needed a boat to reach Ireland. Julius Caesar described the group of islands as British in 55BC. We follow Caesar's usage - and sympathize with anyone who is unhappy with it. Since the pre-Roman islanders were non-literate we do not know what names they used for their homelands. The Romans occupied all of England, some of Scotland, some of Wales and none of Ireland. After the 5th century AD large areas were settled by peoples who spoke Germanic languages. Christian missionaries came to England from Ireland and from France. British missionaries later want to Germany. An Anglo-Norman invasion of Ireland took place100 years after the 1066 Norman conquest of England. After 1603, there was a determined attempt to use the term British (and Great Britain) to refer to a 'United Kingdom'. In the preceding century, 'British' tended to mean 'Welsh'. Dr Johnson gave the following definitions of British: (1) what relates to the land where we live (2) Applied to language, it means the Welsh'.
The Scots parliament was in abeyance from 1707 to 1999 and Scotland was sometimes called 'North Britain' (the hotel beside Waverly Station used to be known as the North British Hotel). The term Great Britain was used specifically for the 'united' kingdom while British Empire included overseas colonies.
Today 'British' tends to be regarded by nationalists, in Ireland, Scotland and Wales as an unwanted name for a short-lived empire. But if the group of islands is not described as British it is difficult to think of any other name. Geographers would be in a better position if the empire, like the language, had been described as 'English' - always remembering that this term derives from the 'Angle' - a region south of Jutland (Denmark). Since the English Empire in the British Isles was established by conquest this would not be inappropriate. The initial conquest of the British group of islands was extended to 'a quarter of the globe' by 1914 but had shrunk enormously by the end of the twentieth century. By the standards of world history the manner of its acquisition and subsequent disassembly were comparatively civil. The 'Union Jack' flag was made by integrating the flags of constituent nations.