James I

James I of England, known in Scotland as James VI, succeeded Elizabeth I in 1603, and continued her Protestant reforms. According to the Eighth Doctor, his accent was so thick, members of his new English court required a translator. A close advisor to the new king was William Lethbridge-Stewart, an ancestor of Alistair Gordon Lethbridge-Stewart. (NA: The Dying Days, NA: Birthright) An influential version of the Bible was ordered by him, and eventually bore his name. The First Doctor and Vicki Pallister once passed by the room where the translators were busy working on what would become the King James Bible. According to Barbara Wright, James' rule was characterised by relative religious tolerance. Though a staunch Protestant, he discouraged persecution of Catholics. Barbara claimed that he realised that "to govern well it made sense to unify people rather than drive them apart." (MA: The Plotters)

For a brief time, the TARDIS came into James' possession, but he was mostly annoyed by it, calling it a "wooden puzzle box" because he and his courtiers could not gain entrance to it. In the end, he entreated the Doctor to perform an exorcism upon it, just to ensure it was not possessed of evil spirits. The Doctor agreed, and performed an elaborate ceremony at the Guildhall in London. During the middle of this ceremony, eagerly attended by James, the Doctor and his three companions entered the TARDIS and dematerialised. (MA: The Plotters)

Upon his death in 1625, he was succeeded by his son Charles I, who ruled England, Ireland and Scotland until his execution on 30 January 1649. (PDA: The Roundheads) More than sixty years after his death, his grandson James II was overthrown in the Glorious Revolution in November 1688. (CC: The Glorious Revolution)

Behind the scenes
In the real world, there's some question as to whether the title James I of the United Kingdom would be appropriate, since the United Kingdom was not technically formed until 1707. He is most often styled, James I of England and James VI of Scotland. However, the Eighth Doctor specifically calls him James I of the United Kingdom in The Dying Days.
 * According to The Brilliant Book 2012, a non-canonical REF book; In 1605, James encountered the Eleventh Doctor's companion's, Amy Pond and Rory Williams on their honeymoon. Because the Tenth Doctor had taken the virginity of his cousin, he tried to have them arrested and thrown in the Tower of London after Rory told him of their friendship with the Doctor.