King William II William Rufus
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King William II (William Rufus), who reigned from 1087 to 1100, was the third son of the famous William the Conqueror and was his chosen heir. William II, called "Rufus" for his reddish complexion, never married or fathered children, leading to speculation that he was gay. His closest adviser was Ranulf Flambard, who eventually became bishop of Durham, and William was often in the company of attractive men, notes the website Historic UK, which concludes that we'll never know William's sexuality for sure.
William had a contentious relationship with the Roman Catholic Church, England then being a Catholic country, but he was known as a strong military leader. He had enemies within his family, however. He died when shot in the back by an arrow during a hunting trip; his death may have been accidental - or it may have been engineered by his brother Henry, who quickly had himself crowned king, becoming the first of many Henrys on the British throne.
King Richard I (Richard the Lionheart)
King Richard I (Richard the Lionheart) reigned from 1189 to 1199. "His knightly manner and his prowess in the Third Crusade (1189-92) made him a popular king in his own time as well as the hero of countless romantic legends," notes Encyclopedia Brittanica. "He has been viewed less kindly by more recent historians and scholars."
He was a savvy politician and military leader who also wrote poetry but was "capable of great cruelty," according to Brittanica. There is significant evidence that he was gay, although historians differ on this point. He had no children with his queen, Berengaria. Richard has been frequently portrayed on stage and film; The Lion in Winter (1968), in which he was played by Anthony Hopkins, strongly suggested he was gay, while Sean Connery offered a thoroughly heterosexual depiction in Robin Hood: Prince of Thieves (1991).