"You are even more handsome than your portrait!" - King of Portugal to Princess Margaret Tudor
The unnamed King of Portugal is briefly Princess Margaret Tudor's first husband (the second is Charles Brandon, the Duke of Suffolk). Margaret is repulsed by her old husband and smothers him to death after a few days.
The King of England, Henry VIII, organizes a wedding-alliance with Portugal between his sister, Princess Margaret Tudor, and the elderly King of Portugal. Margaret, disgusted, requested that Henry promise her that after the death of the King she will marry who she wants. During the trip of Portugal the Princess has an affair with the charming but womanizing Charles Brandon.
At the Portuguese court, Margaret meets her husband, who is very perverted and almost crippled by gout. Following the wedding, the marriage is consummated, to the shock of the new Queen.
Terrified and furious, a few weeks later Margaret smothers the King with a pillow; he is succeeded by his son, who seems pleased to finally be taking the throne. Afterwards, she returns to England with Charles.
In real life King Henry VIII had two sisters, Margaret and Mary, but the writers for The Tudors didn't want to confuse the latter one with the Henry's elder daughter, Princess Mary. Mary married an elderly king (actually Louis XII of France, who died of gout) and after his death married Charles Brandon, whereas Margaret married the King of Scotland during the reign of her and Henry's father, Henry VII. The Margaret of the series is essentially a combination of Margaret and Mary.
While the timeline of the episode is confusing (Mary (Margaret) went to France (Portugal) to marry in 1514, Henry VIII was awarded the title of Defender of the Faith in October 1521, King Henry's jousting accident was in March 1524, and his failed attempt to pole vault a ditch was in 1525), the King of Portugal at the time (1510s-1520s) was either Manuel I, the Fortunate (who died in 1521 at the age of 52) or John III, the Pious, who succeeded his father at the age of nineteen and would be around that age at the time of this episode.