The King of Britain was the title given to the ruler of the country of Great Britain.
In 924, the coronation of Athelstan occurred and he, according to the Tenth Doctor, became the first King of Britain. (TV: Planet of the Dead) His predecessors, Alfred the Great and Edward of Wessex, had united the smaller kingdoms of England during their reigns. (PROSE: The Man Who Wouldn't Give Up, AUDIO: The Lady of Mercia) However, there was still a separate King of the Welsh by Athelstan's era, Hywel, (TV: Planet of the Dead) and Wales was absorbed into Britain in the following centuries. (TV: Boom Town, The New World) Many other accounts stated that England continued to exist as its own state for many years after the 10th century.
After the death of Elizabeth I of England in 1603, the throne passed to James I, who was already the King of Scotland as James VI. The Eighth Doctor said he became "James I of the United Kingdom" at this point (PROSE: The Dying Days) but others held that the two nations were still separate, along with Ireland, which was also ruled over by the Kings of England. Except for roughly a decade during which all three domains formed a Protectorate led by a Lord Protector, (PROSE: The Roundheads) the throne remained with the Stuarts until the death of Queen Anne in 1714. (AUDIO: Doctor Who and the Pirates)
Eventually, the English were "alienated by the autocratic Scottish Stuart Kings" and threw them out of the "United Kingdom", replacing them with the Hanoverian German Georges. George I was succeeded by George II, (PROSE: The Highlanders) who was then succeeded by his grandson, George III. (PROSE: The Wheel of Ice) By the 1790s, the nation he ruled was "the Kingdom of Britain". (PROSE: The Adventuress of Henrietta Street)
By 1879 and the reign of Victoria, Britain had formally united with Ireland and she described herself as the "Queen of the United Kingdom of Great Britain and Ireland". (TV: Tooth and Claw)