In 1701, the British parliament promulgated a new succession law , called the Act of Settlement, which devolved the succession on the Protestant descendants of the Electress Sophia of Hannover. This was done because William and Mary had no children, and none of Queen's children survived childhood or infancy. The next in line to the throne (who was not Catholic) was the Sophia, the 13th and youngest child of Princess Elizabeth of England and Scotland, who married the Elector Palatine of the Rhine. Elizabeth was the daughter of James I of England (and VI of Scotland). Elizabeth's brother, Charles I succeeded James I. Charles I was succeeded by his eldest son, Charles II, who had no legitimate issue. Charles II was suceeded by James II, who had two daughters, Mary and Anne, by his first wife. He converted to Roman Catholicism, and his second marriage was to a Catholic, Mary of Modena. It was in 1688, after Mary gave birth to a son, who was baptised Catholic, that Parliament took action. (There were other factors that led to what is known as the Glorious Revolution, as well). James II and his family fled, and Parliament invited James' elder daughter, Mary and her husband (and first cousin) William of Orange) to be joint rulers. Mary died only a few years later.
Thus, in 1701, Sophia became the heiress presumptive to the British throne (as of 1707 with the Act of Union). She died in 1714 only a few months before the death of Anne. Thus, when Anne died, the throne passed to Georg Ludwig, Elector of Hannover. (Hannover did not become a kingdom until 1814).
He preferred Hannover, but George I also realized that Britain was a more important kingdom ...the family retained ties to Hannover, but there was a lot more prestige and power as king of the UK of GB and Ireland.
There was no need for European nations to quarrel over who would succeed to the British throne. In 1701, Georg Ludwig was well aware of the fact that he would one day succeed to the throne. It was a done deal - and England was one of the most powerful, if not the most powerful nation in Europe, having won numerous battles, thanks to the brilliant leadership of the Duke of Marlborough.