Gaelic culture was pushed west and north, Latin was on until Anglo-Saxons mingle-controlled the islands and called them England. The Normans came over from Bretagne and took over the estate, recorded in the Doomsday Book. Magna Carta was developed to control the conglomerate of cultures that became Great Britain. The United Kingdom is a superstructure on top of the underlying britishness. Britain is a replacement term for England unless one is formal.
Great Britain and Britain are Norman names for the Bretagne rulers. 1066 forever!