This certainly isn't more relevant than the TV version. Also I question the use of "King" in the title. I suggest Arthur (The Creation of Camelot)
Talk about it here.
Needs to mention suggestions that Arthur was not real in the main universe, as per Battlefield.
According to one source, The Doctor once pulled the sword from the stone and handed it to Arthur, instead of leaving Arthur to do it himself. The Doctor was therefore made King of England but he abdicated after a day in Arthur's favour. The Twelfth Doctor refused to take Clara Oswald to meet Arthur as he considered this incident a bad time. (PROSE: Silhouette)
A year after the Master arrived, Arthur's son Mordred was born to his half-sister Morgan at Lothian. Arthur sent the Master to kill Mordred. He was unaware that the Master had instead helped Morgan in raising him. The Master planned for Mordred to kill Arthur at the battle of Camlan so Britain could never become one country. The Master pretended to be an enemy of Morgan to fool Arthur. (PROSE: The Creation of Camelot)
Arrival of the Doctor
When the Fifth Doctor and Tegan arrived, they were put into a cell by the guards. Eventually, Arthur came to meet them and set them free. When the Doctor told Arthur about his TARDIS, Arthur told the Doctor that the Merlin had mentioned such a thing.
The Doctor realised that the Merlin could only be the Master in disguise. Arthur sent for the Merlin . The Doctor and Tegan soon recognised him. The Master tried to convince Arthur that he was no threat and he still served him. Arthur, convinced by what the Doctor told him, had the Master sent back to his room and put on trial. However, he was unaware that the Master's room was actually his TARDIS.
Behind the scenes
As in the real world, King Arthur's categorical existence in the Doctor Who universe is debatable. Some sources, such as Battlefield, claim Arthur is mythical. Others, like The Creation of Camelot, regard him as a real historical king whom the Doctors have met.
Stephen Fry's unproduced script, The 1920s, was based on the Arthurian legend of Sir Gawain. The Fisher King in Before the Flood is named after the eponymous Fisher King in Arthurian legend, who, like the Doctor Who character, is in need of aid to be restored.